Basically all geometry calculation happens with triangles internally in all major 3D apps so madefun3d is right.
Its just that in modeling apps like for example 3ds max etc. you have the option to not view the mid edges if working with quads is what you need, but basically those mid edges are still there but hidden from view.
For example in 3ds max you can switch on edit tri mode to view those mid edges and turn them if necessary.
Personally I prefer to work with tris if it involves game models as one can maximize the topology of the model more easily (I mean better determining placement of the points and edge flow), working with quads on game models it is not always that obvious to see when a hidden edge would be better placed in one or another direction to contribute better to some aspect of the contours, and constantly switching to view the hidden edges is not that practical.
Tip if you work with 3ds max:
In 3ds max you can go to sub-object level vertex and select all vertices in the model, then simply hit connect and then all edges become permanently visible. Alternatively you can also switch your model to edit mesh type, then go to sub-object level edges and hit select all (the mid edges would now also be visible as dashed lines), then scroll down to surface properties and hit visible, this also permanently makes those hidden edges visible, now you can switch back to edit poly type with all edges permanently visible.
Quad editing is actually meant for sub-d workflows as it gives better visual feedback as to avoid areas where more edges would flow to one vertex (would produce continuity problems in edge weights and introduce bumps in the mesh division and finally distortions in ray traced reflections etc.), this problem is not an issue in game engines as one would provide smoothing information through normal maps.
About the poly count in game characters, I would also add that it is important to know how much of unique characters would be visible in the scene at any given point. For example if you have allot of unique characters with lots of details and they would all come together at same spot (need rendering in same frame) that could hit performance. You basically have to bring everything into account when you absolutely want to max out on everything (witch almost never gets done). Having that said I think for a PC game 30 to 60.000 triangles is good average to make something that is visually descent and if there is headroom left then maybe spend it on more stuff to put in the scenery or stuff that can be added for ultra settings.
From a standpoint of a 3D stock media developer these are variables that cannot be known as they are the decisions of the game developers and there unique use cases, but we can make different versions of the same model varying poly count/details to accommodate the different possible scenarios and widen possible appeal to different use cases.
