You don't seem self-aware of your plan.
Alright, so you want to build an NFT Game, but with Bitcoin. Do you know that Bitcoin isn't
turing-complete? You'll have to work on a project that is, such as Ethereum.
Are there any LN BTC driven NFT games? Are they any good? If not: Why?
Do you mean games that accept the LN BTC as a payment method? There aren't probably many. But, here's another advantage of bitcoin; it doesn't have to. As long as there are people willing to exchange gift cards for bitcoins, you can use the lightning network to make in-game purchases.
This is also true for online services such as Google Play, Spotify, Netflix, Steam etc. They don't have to accept cryptocurrencies as long as there's this intermediary.
Call me a hater, but I prefer my Games to use real money - not premined shitcoins. We already got some of these, we call them Dollars.
Well, that's where these projects lack of. While they are cool as concepts, they fail in the sociopolitical part.