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.
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.