Have NES Game Prices Peaked

It will probably continue to increase. No more are being produced, and the more worthwhile ones are being added to collections and taken off the market, so what's left on the market is increased in pricing. Some also become lost or destroyed over time. It may come down when buyers are no longer interested - maybe that means the people who fondly remember NES games have passed on, so this would take a while.

Just wanna point out you're asking people to predict the market

Can it go up? Of course!

Has it peaked? Maybe

Peaked? No, probably not. Stabilized? Possibly. Falling. Maybe? Just keep your eye out for a good deal.

My rule is - If it's worth it to me for that price now - it will almost assuredly be worth that to someone else later.

I think it can keep going up.

Don't forget to include inflation. In the US it's more than 75% since the year 2000.

Peaked? No, not unless another production run happens. They will fluctuate, but you should have every expectation that 500 years from now, an original cartridge of Mario/Duck Hunt will be pretty damn valuable. Much less the actually rarer ones that will have stopped existing outside of digital and pirated physicals.