War2 is about space management not so much about army composition what you loose in units diversity you win in terrain and space management.
Units in war2 are all about managing that space and controlling that big grid.
War2 has 14 units per race which is not so far from what other games have to offer which is around 15.
The only difference is you do not specialize your army in war2 you do not ignore half of your tech tree because you committed to the other half.
In war2 every unit is used at high level and has things it does better than the others.
Short example:
peons gather land resources and build
Foots costs no wood and are cheap
Archers are the quick answer to things your current units cant do like defending a wall killing a few dragons to buy you time to get a better counter.
Ballistas are the siege unit they are a quick answer to battleships and towers before you get mages
knights and ogres are the strong melee units for mid game
Griffons are the air units that only can be addressed properly by mages if they are too many
Mages are the answer to almost everything but knights.
Sappers are the units to blow up terrain or walls.
Oil tankers are the workers of the sea
Transports the only way for you to move your ground units accross sea.
destroyers are anti air, anti transports and very fast water units.
Sub marines are invisible and a pretty good counter to an all in hall battleship army or a good answer to transports when combined with zeppelins because they will always hit their target even if it is fast.
battleships are the long range strong water units they are water domination units but they cannot address air.
Because of that in long hsc games you may see all units being used by all players, remove just one of these units and you have yourself a big handicap.
So even if I really like aoe, starcraft and war3 I would not argue that because they have more units they are more strategical.
They are just very different games overall with much more focus on micro managing your units and not as much your space. The worst being war3 on that matter.
Lone is right in that way.
Maps variety is indeed a good way to see how much space affects the game-play.
Another way to put it is:
Although Chess has more pawn types than Go, it is not more complex nor more strategical than go as a matter of fact it is way harder and more complex to create an AI for Go than chess.