The beholder having no use for the antimagic cone is kind of a good thing for this fight, as it means it can actually use its eye rays on the target to their fullest potential.
It might also be important to note that beholders are like the ****** up inbred children of the cast of Doomsday Preppers and a super computer. They're so ludicrously paranoid that, when combined with their staggering intelligence, they prepare for pretty much any scenario. To quote Volo's Guide to Monsters, "It doesn't matter if invading adventurers arrive at its lair with summoned angel allies or enslaved demons, by breaking through the floor, by teleporting or riding dinosaurs, or girded with layers of magical defenses and armed with advanced weapons. In any case, the beholder's reaction is calculated, because it has thought about what it and its minions must do in response to every situation."
Basically, it doesn't matter that a 2-D man has just barged onto this floating platform and started flipping pancakes at the beholder. It was already at least somewhat prepared for a similar outcome due to its own insurmountable paranoia, and if there's any chance it can outplay Game & Watch (which there almost certainly will be), the beholder will take it in a heartbeat.
Coupled with the fact that the beholder's most dangerous abilities can outrange G&W, before even adding the fact that it can just endlessly hover, I see this swinging pretty damn heavily in the beholder's favor.
I don't believe G&W really has a counter for mind control/empathic manipulation, paralysis, suddenly being overcome with crippling fear that stops him from approaching his enemy, having his speed cut in half, being put to sleep, being completely petrified, having his whole body reduced to dust, and a ray that simply says "looks like you were dead the whole time, bucko" before turning him into a corpse...especially when all these things are coming at him at once from a creature that can see in all directions. All the while, somewhere in the back of its mind, the beholder's been preparing for a fight like this its whole life.
