No. That's a communication job, a joint activity. It's impossible to play a
multiplayer game with someone else using only software on your computer.
If the game was single-player, and the server only existed to provide the
game world... that still probably wouldn't be SaaSS, because in that case
you're accessing the server to get the particular game world.
Really, the only case of SaaSS in games is things like the OnLive; so-called
"cloud gaming", where the game runs on someone else's computer and you send
input to the server while the server sends you a video feed.