How is this legal? Specifically, distributing copyrighted assets and using their name/logo without permission.
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As I understand it, Lego is aware of the project (there's been a significant increase in interest in Lego Island in the past few years, with attempts to obtain the original source code) and simply does not care. It's an ancient IP and can't realistically compete with anything new, at least not in a way that would significantly affect Lego's revenue. This is not unlike the way several other companies have acted when their respective older games have been given the same treatment; if a fan project is not actively causing problems (reputational, financial, etc.), most companies will just leave it alone. For companies that actually seem to care about public opinion (as opposed to, say, Nintendo), I think it's fair to assume that the bad optics of taking legal action against a random fan project, however legally justified it might be, far outweigh any possible benefits.
Once fan projects get too much traction, companies have to cease and desist them because that's the way intellectual properties work in the law. It usually has nothing to do with whether it was a cool project or not, it's just that there's way too much money at stake when not defending your IP.
That said, Lego doesn't own the game, so if it came down to it, they could strip all the references to "Lego" from it and probably be fine.