Well, the last statement in the question is true (you don't see Geordi play) but we know he DID play it, from from the episode transcript.
After they report Data as being inactive and LaForge tries to figure out what happened. The last lines of how they reeled in LaForge to play the game:
[Data's quarters]
RIKER: Standard security sweep shows nothing out of the ordinary. LAFORGE: Personal logs, diagnostics, duty logs, they all appear normal. There's no evidence of anything that could lead to Data's shutdown. RIKER: Maybe we should ask his cat. LAFORGE: I guess I'd better get back to Sickbay, see if there's any change in his condition. RIKER: Doctor Crusher's got everything under control, Geordi. If there's any change, you'll be the first to know. LAFORGE: I guess so. RIKER: Looks to me like you need a break. Unwind a little. LAFORGE: Yeah, maybe you're right. RIKER: I've got just the thing. Why don't you join me in Ten Forward? There's something I'd like you to try.
And later, on Wesley's and Robin's date, we get confirmation that Geordi did play it:
[Ten Forward]
WESLEY: Sounds kind of lonely. Well, now you're here.
ROBIN: Now I'm here.
WESLEY: Well, I'm glad.
ROBIN: You wouldn't believe what's going on in Engineering.
Commander La Forge and all the others,
they're crazy about some new game.