For starters, game engines themselves only use triangle geometry. I think it is because it's the only geometry it can read, but I am not sure about that.
People (Like myself) stress a lot about the use of triangles, because you generally want to avoid them. Triangles aren't totally bad, but can deliver problems.
1 - You want a clean topology as best as possible, but tri's break your topology.
2 - tri's can deliver shading problems and with some modifiers like subsurface division.
3 - if you want to make an animation, it could deliver nasty deformations you don't want.
What you want to ask yourself is;
- Is it a hardsurface object or rather an organic object?
- Am I going to make an animation for my object?
- Can the player see the specific surface well?
Tri's are an effective way to reduce vertices count, but you can not place them willy nilly all around your model. There needs to be a logical reason to place it and not because you didn't see any other solution or it was easier that way.
I hoped that helped a little bit.