Is this footnote from one of Perelman's papers meant to be a joke, or is it mandatory to list one's source of funding?

Indeed, funding agencies require authors to acknowledge their funding, but it's not mandatory to acknowledge personal resources.

To me, however, that footnote doesn't sound like a joke at all, but a sincere acknowledgement of those who have supported him during previous years allowing him to have savings (and during those visits he might have worked on different topics).

That said, there are certainly a lot of joking acknowledgments around.

I find the dichotomy of your title question a bit strange.

No, one is not required to acknowledge personal funding sources, but in academic papers one often acknowledges / otherwise thanks people and things in the absence of any requirement to do so.

Though I do not know Perelman personally, I know him by reputation: he is a person of great integrity. It is not a joke to thank people and places that supported you, especially if you have (by choice or otherwise) modest financial means.

I suggest that this footnote of Perelman's be taken at face value, as an expression of gratitude, which (like most expressions of gratitude!) was not required to be made.

No, it isn't required to list your own personal resources.

But whether it is a joke or not you should decide for yourself. Perelman has interesting views. He has declined a Fields Medal, for example.