Yes, "Game x" means "Home Game x."
Perhaps the Nationals should have taken a lesson from the way the Capitals used to do it by using letters instead of numbers to avoid ambiguity—"Home Game A," etc. I would have thought anyone buying tickets, especially via a presale, would be savvy enough to know that they're only selling tickets to home games and that the game numbers therefore refer to which home game it is (and indeed the presale e-mail advertised this fact), but I suppose you should never underestimate how easily some people get confused.