Some general points about frame size
It really depends on your body proportions (for example long arms and torso, but short legs, or long legs and short torso, etc.), and your flexibility, how easily you can extend your legs and bend your back. Your height alone is not enough to decide ideal frame size.
I'm 1,87 and ride a 54.5 with 120mm stem road bike.
And Chris Froome for example is 1.86 and rides 55mm effective top tube. But these are road bikes, and by design the handlebars of road bikes have longer reach. My MTB, on the other hand, has 58.5cm effective top tube and 90mm stem. So, if I add the two together it equals 67.5cm, only 1cm longer than what you have, even though I'm 13cm taller. So my frame might be even more strongly regarded as "too small" for me by various online charts, yet I'm perfectly comfortable.
For some people it works to have a smaller frame. If it works for you individually, a good bike fitter can decide. Or you can study your position in more detail, film yourself from the side on a trainer, and try various adjustments to see how it feels. You could also rent another bike and see how it feels. If you want to do a bike fit for yourself, there's a book written by Phil Burt that you may find helpful.
For road bikes, another measurement that affects the overall reach is the handlebars' reach, and the brake levers position on the bars. If you move the brake hoods forward on the bars, lower, and then rotate the handlebars back at the stem, you can effectively increase the reach by around 1 to 3 cm. Or you can find handlebars with longer reach.
Usually it's when the reach is too long that people feel discomfort.
I can think of some bike adjustments that can make the bike feel like the reach is too short when in fact it isn't:
- Is the saddle tilted down too much, causing your pelvis to slide forward?
- Is the saddle fore/aft set all the way, or too much forward?
- Is your handlebars width correct? I.e as wide as your shoulders, on a road bike;
- Is the saddle too wide, forcing you to sit more forward on it?
- Are your handlebars too low, with no spacers under the stem, and/or the stem flipped down? This could also cause hip impingement and pain;
- Is the crank arm too long, and you feel the need to move forward to be on top of the pedal at 3o'clock, the power phase? This can also cause hip pain.
- If you are using clip-in pedals, are the cleats set too far forward on the shoe? When we push on the pedals, there is some reaction force that pushes our bodies back towards the rear of the saddle. If we move the cleats further back, and push on the pedals using more of the middle part of the foot rather than the toes, then this effect is increased. A rear cleat position is always considered safer and more ergonomic. But this will also affect seat height, because it changes the effective leg length. So if you move the cleat back by let's say 5mm, then you should lower the seat height a little bit, let's say 10mm.
In response to the video of you on the bike
I don't see anything extremely wrong with your position, I think you can make that frame size fit. There are, however, some observations and tweaks I can suggest, based on what I've studied online about bike fitting.
Indeed, the reach of the bike seems a little bit short. But nothing crazy. I don't think a longer reach will necessarily help. In general, increasing the reach has these effects: a) it puts more weight on your hands and shoulders; b) it closes down the hip angle, because you lean your torso forward more, the knees will have to come closer to your chest at the top of the pedal stroke, and people with not very good hip mobility find this uncomfortable;
Your torso is fairly upright, and the hip angle open, you seem to have no trouble raising the knees and getting through the top of the pedal stroke. I think you can tolerate a longer reach, but it doesn't necessarily mean it will solve your issues. It may make them worse;
The saddle height seems a little bit high. Doing a rough measurement of the knee angle on the video shows about 150 degrees knee extension, or 30 degrees flexion (away from full extension).
This dynamic knee angle is recommended to be in the range of 35 - 40 degrees from full extension in Phil Burt's book (or 145 to 140 measured from these body markers: 1. great trochanter at the hip, on the femur; 2. lateral epicondyle at the knee, still on the femur; 3. lateral malleolus at the ankle, on the fibula). Other bike fitters recommend an even wider range of 33 to 48 measured dynamically (while you pedal). People with poor hamstring flexibility usually need a lower saddle. You can do this test, or other similar flexibility tests for the hamstrings and see how you compare. 
With an optimum saddle height the pedaling motion should feel smooth and fluent all the way around, without excessive tension behind the knees, and without the need to rock the pelvis from side to side on hard efforts.
The ankle also plays a role in saddle height. Several studies showed that changes in saddle height are mostly absorbed by the ankle (people compensate for a high saddle by pointing their toes down, and for a low saddle by dorsiflexing the ankle back). So, in theory, people with a high range of ankle mobility tolerate a larger range for saddle height, while people with stiff ankles have a narrower range in which they feel comfortable. An ankle flexibility test is presented in this video. In your video, your ankles look nice and stable, in a neutral position. But this is on a flat road at easy pace. When going uphill at a harder pace for example, people tend to dorsiflex the ankles, and saddle height should be set to allow for this, i.e not excessively high.
I see you are wearing a backpack. On long rides it may put too much tension on your body, and may make small issues worse, especially if the straps keep sliding off your shoulders (when you reach for the water bottle for example, or when standing on the pedals and rocking your body left and right) and you feel the need to shrug, and keep constant shoulder tension, to prevent it from falling. I, personally, cannot tolerate a backpack at all on the bike. On long rides I carry all I need inside a frame bag between my legs + a saddle bag (under the saddle). If water sources are scarce along your route, you can get a bigger bottle, or try to fit a 2nd one under the down tube, even if the bike comes without dedicated mounts, there are strap-on adapters.
What changes I suggest for you to try
- Try a lower saddle height, it is generally safer. I estimate a 3cm drop from what you have now will bring you more into that recommended range. You should be able to place your heels on the pedals and spin at an easy pace without losing contact with the pedals at the bottom, and without the need to shift left and right on the saddle. This bike fitter recommends starting low and working from there.
- Move the saddle all the way back. This will: a) reduce the weight your hands and shoulders need to support, and make your upper body feel more relaxed; there's this test you can do; b) take some tension off your legs as well, and make the pedaling motion easier, as more of your weight will be shifted back and be supported by the saddle.
On the bike your body weight is distributed among the 3 contact points: saddle, pedals, hands. I believe you are putting too much weight on your hands and legs and not enough on the saddle because it is too high and forward.
Note: You may be used to riding in your current position, and any changes that you make might feel wrong at first. You should give your body some time to adapt to the new changes, a few easy rides on the course of a week or two. Don't do very long or hard rides immediately.
About Knee Over Pedal Spindle (KOPS) method
The KOPS method doesn't seem to have good biomechanical reasoning behind it, and it is popular mostly by repetition, and many bike fitters criticize or disregard it completely, like this one, or this one.
There's nothing wrong with having your knee behind the pedal spindle. And given your chondromalacia, I would set it as far back as it goes, to reduce the load on the knees. This effect can be seen off the bike as well, for example with the lunge exercice. Try and do a lunge with the knee more in front of the toes, and then move the knee further back. You will notice the tension on the knee goes down as you move it further back. This video demonstrates.
Midfoot on the pedal
Another thing that many bike fitters consider to reduce the load on the knees while pedaling is to use the middle of the foot (or as far back from the toes as possible) to push on the pedal. This reduces the tension of the calf muscles and the forces that go through the knee. But to be able to do this, a low enough saddle height is required. You can do a little experiment off the bike, climbing some stairs using only the front part of the foot, and then again but with the entire foot down, and see which feels more comfortable to you. This video demonstrates something similar.
Low gear high cadence
What is also recommended to reduce the load on the knees is to use lower gears but higher cadence. If you find difficult to spin at 90rpm for more than a few minutes, it might be an indicator that the saddle is too high. When the saddle is too high, the tendency is to apply the power in impulses at a lower cadence, rather than smoothly and fluently across a larger portion of the pedal stroke using a higher cadence.
