A game on war is a wargame no matter the platform and of course WiC does count. Axis & Allies is a wargame as well...the question is whether a game is a conflict simulation or not. A&A is certainly a wargame but no consim, I haven't played WiC yet so can't say whether it's a wargame or a simulation.
It falls more under the real time strategy genre than wargame genre, but it sure does look pretty. It follows the same basic rock-paper-scissors combat system where each unit has a counter, and there isn't any difference in the game strength wise between say a T-80 and an M-1.
I have enjoyed it though, and if you have a nice system, watching Tactical Aid get used in the game is great. WiC was the first title I loaded when I built my new system at the end of July. You have everything from pgm strikes, artillery, and napalm to fuel-air explosives, chem strikes, and nukes. Sometimes it is hard to concentrate on playing the game because it is so entertaining to watch it unfold.
It falls more under the real time strategy genre than wargame genre
I don't see how you can say RTS games are per se not wargames. A wargame is a game on war, it's that simple. RTS is a specific mechanic of gameplay nothing more. Even Call of Duty 4 is a wargame and it makes no sense e.g. to say 'well no its a FPS'. Whether a wargame is a consim or not is a different question, though.