Current games definitly do use height map methods. Depending on the type of game some might not but there are some that definitly do and some that will use a blend of different methods. For example one that does use height maps woiuld be the Delta Force Series, going to even the current day versions. As for GTA3 well I'm not sure, if it does then it would be a mixture of other methods too, the way you shoudl see it is if at any X,Y position there will only be one height then a height map is suitable. But if you want over hangs or anything like that then they aren't the best choice.
I should add in actual games I'd imagine BMP files aren't used but the raw format you just mentioned .

It al depends on the game really and theres no definite way to do it and fit every game. Using height maps is just a theory in a way because it can be implemented many ways and the basic definition would be that your using a list of numbers in a grid fashion to define the height of a selected area.
For example (this is probably not the way its done but a possible way) in GTA you could have all the roads made with a height map. Like a stright image with width the same as the road and length very long. you could then "bend" that height map around the route that the roads take to give you their shape. This is most likely not how then've done it but I'm just trying to show how meight maps can be used in many different ways. That example would be pretty limited cause it would have difficulty with anything other then one road that has no junctions in .