In "The Game" an addictive video game is played by everyone on the Enterprise. It communicated with the player's brain via the eyes.
How did it work for LaForge who wears a visor? I don't think I have seen him playing the game at all.
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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.
1) 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.
2) 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.
Since the game works by laser shining on the retina, it is a bit curious how it'd work on Geordi's implant, but it obviously did.
Here's a quote from the transcript, when Wesley and Robin are analyzing the game:
WESLEY: I've loaded the neurological behaviour programme. This sensor pad should allow the computer to process whatever information the game sends at it.
ROBIN: Let's see what happens.
ROBIN: It's activating the reticular formation.
WESLEY: There's heavy synaptic activity all over the place.
ROBIN: I wonder what happens after prolonged exposure?
WESLEY: Speed up the processor and we'll find out.
ROBIN: The effect seems centred around the frontal lobe.
WESLEY: Computer, enhance frontal lobe, full spectrum.
ROBIN: It's stimulating the septal area.
WESLEY: That's the pleasure centre of the brain. Whatever this thing does, it must feel pretty good.
ROBIN: No wonder it's so popular.
WESLEY: Look at this. Serotonin levels are way off. Let's run a neurochemical analysis.
ROBIN: I'm seeing widespread bonding to neuro-receptors.
WESLEY: Correct me if I'm wrong, but this looks like a psychotropic reaction.
ROBIN: Are you saying you think the game's addictive?
WESLEY: What's going on in the prefrontal cortex?
ROBIN: Doesn't that area control higher reasoning?
WESLEY: Yeah, it sure does. I'd better go talk to the Captain.
None of the terms mentioned have anything to do with the eyes. Most of them are parts of the brain - so the game itself was probably just a distraction, a reason to keep playing while the machine affected the brain directly. The bursts of pleasure had to sync up to what was happening in the game, so that the person had a reason to keep playing at the conscious level, besides the addiciton.
That would mean it would indeed work on Geordi, if he wore it long enough. He probably modified his VISOR in some way to be able to see the game, or was simply held down by Riker like Wesley was near the end of the episode.
This makes me question how the solution at the end of the episode would have actually worked, when Data enters the bridge. So there is an alternative explanation, where we keep the effects limited to entering through the visual nerves: It just does. The VISOR is hooked up to the working parts of Geordi's visual nerves, bypassing the eyes. While he does see everything very differently, it is fed through his visual cortex like regular humans.