So one could argue that it was a plot device or that the jury simply found that there was insufficient evidence to convict. Let's look at what UCMJ Article 118: Murder says:
Any person subject to this chapter whom without justification or excuse, unlawfully kills a human being, when he- –
(1) has a premeditated design to kill;
(2) intends to kill or inflict great bodily harm;
(3) is engaged in an act which is inherently dangerous to others and evinces a wanton disregard of human life; or
(4) is engaged in the perpetration or attempted perpetration of burglary, sodomy, rape, robbery, or aggravated arson;
is guilty of murder, and shall suffer such punishment as a court-martial may direct, except that if found guilty under clause (1) or (4), he shall suffer death or imprisonment for life as a court-martial may direct.
There is no actual "Murder in the First Degree" charge in UCMJ that I am aware of (or could find), instead murder is murder, whether it was premeditated or caused by other unlawful acts. Note that causing a real accidental death (e.g. if you lose control of your vehicle and hit someone) is still Manslaughter rather than Murder.
So my first point is that it's a Hollywoodism to begin with, since they charge them with a crime that doesn't exist in UCMJ.
If they were actually charged with Article 118, would it have stuck? Well, that's more challenging to say as viewers of the trial. Let's try the various tenets of the Article:
Any person subject to this chapter whom without justification or excuse, unlawfully kills a human being, when he- –
OK, so they are active duty Marines (therefore subject to this chapter), the jury ruled the "we were following orders" didn't give them justification or excuse, and it's established that they killed a human being unlawfully.
The 4 points are all "or" statements:
(1) has premeditated design to kill;
Ok, no, it's established they didn't plan on killing Santiago just roughing him up
(2) intends to kill or inflict great bodily harm;
This one is more debatable, but I think we can again assert that they definitely didn't intend to kill, and probably didn't consider what they were inflicting to be 'great' bodily harm. Certainly, there was nothing in what we saw of the trial (recall that we don't get to see every second of it) that establishes beyond a reasonable doubt that they intended to do more than scare the kid.
(3) is engaged in an act which is inherently dangerous to others and evinces a wanton disregard of human life; or
So this one I could actually see sticking, depending on how the lawyers argued it and what kind of off-camera evidence was presented. That said, it could have been established that based on other cases of Code Reds that hadn't caused more than bruising, the defendants were not wantonly disregarding human life and could not have expected it to be inherently dangerous. People get bruises in training all the time.
(4) is engaged in the perpetration or attempted perpetration of burglary, sodomy, rape, robbery, or aggravated arson;
Unless there were cut scenes that took a darker turn, these are all "no" as well.
Agree with the other answer that there is no "Conduct Unbecoming a US Marine", but I would say that Article 134: General Article would apply instead:
Though not specifically mentioned in this chapter, all disorders and neglects to the prejudice of good order and discipline in the armed forces, all conduct of a nature to bring discredit upon the armed forces, and crimes and offenses not capital, of which persons subject to this chapter may be guilty, shall be taken cognizance of by a general, special or summary court-martial, according to the nature and degree of the offense, and shall be punished at the discretion of that court.
So again, the change in the name of the charge is something of a Hollywoodism, but if correctly named it definitely could have resulted in the dishonorable discharge that they got.
I should note that I'm not a lawyer, but I've been both a Company and Battalion Commander in the US Army, and so have had to be fairly familiar with UCMJ.