Infinite recursion (without a base case) is still recursion and, with tail call optimisation, can be useful in practice for the same reasons infinite loops can be useful.

I don't really see why the author doesn't see the joke as recursive. If it's about the lack of a base case they're misguided. Maybe the author is distinguishing between functions that recurse by calling themselves directly (direct recursion) and ones that call themselves via other functions (indirect recursion). Or maybe it's about recursive functions vs cyclic data structures. Or maybe it's something else as neither of those explains why the quoted joke is incorrect either.

You'd think in a section titled "Recursion vs Cyclicity" the author would make some effort to explain the difference, but apparently that matters less to them than calling things "dumb".