I don't know. You're not asking for donations to keep maintaining a product you don't own. You're asking for donations as someone who put their services to work.

Consider a tricky grey area: you have a patreon for your youtube channel and expect most people to be donating so you can keep making videos (you get maybe, $50 a month). You also make random mods on the side. One of your mods blows up, and you get a bunch of attention. Which includes donators giving you hundreds thanking you for the mod. Are you now taking "blood money" because your tip jar for youtube content now has financial incentives to make more gaming mods?

I personally treat the tip jar as such. As long as you're not saying "pay me this much and I'll make X mod", I'm donating to a person, not a potentially morally grey cause. Maybe the Nintendo lawyer disagree with me, but that feeling has always been mutual.

What is the service here though, if it's not just "here's a way to play a copyrighted game without paying"?

I'm sure this project took a lot of work and effort, but legally/morally speaking that's beside the point of where the value is and who should be charging money for it.

Would this website still be popular if it was just an online emulator that was capable of playing NFSU2 in the browser, in theory, so long as you uploaded your own legal copy? I'm not sure so many people would be visiting it or posting about it, to me 100% of the value of this site is just being able to play a great game that other people made, for free. The actual emulator itself is almost irrelevant to the value, if you get what I'm saying.

Would many people visit a movie piracy site if it didn't actually have any movies but just had a blank video player that was capable of playing movies, in theory, if you uploaded one you already owned?

Emulators are legally protected and asking for donations is just fine, the fly in the ointment for emulation of modern consoles is that they require firmware and decryption keys extracted from real consoles to actually do their advertised function, the emulator might tell you that it is your responsibility to extract the required files from your own console to protect itself but just like game "backups" it's much easier to download the required files someone else has ripped and uploaded to the internet.

The stupid part was paywalling the latest version of the emulator behind a patreon subscription (it wasn't even effective as anyone could share the latest release) which opened them up to being taken down by nintendo although it was likely they would have been taken down anyway just because the switch 2 was nearing launch and they didn't want switch emulator developers to get started on the switch 2.