The main thing (from a game theoretical standpoint) that I believe sets RTS games apart from (most) strategy board games is not the real-time nature, but the fact that RTS games are not perfect information games.

Incorporating knowledge about your opponent's playing style is important in chess (and I presume Go), but I believe it is vastly more important in RTS games, so much so that in high-level competitive games it is a primary driver of both players' decisions in the game.

Of course, from a broader (not game theoretical) standpoint, the bigger and more obvious difference between strategy board games and RTS games is that the latter, being real-time, requires substantial physical speed and coordination, which is mostly not the case with the former.