Something that hasn't quite been touched upon but might be important to note is that both Zorin and Linux Mint run 'old' kernels (almost two years old in fact). While this does not necessarily have to affect you, there's a considerable chance that you might not reap the benefit from improved performance and other good stuff that would be found on a newer kernel.

Generally speaking, you should be fine regardless. However, if you intend to primarily engage in high-fidelity gaming, then I'd argue it's at least worth benchmarking your performances on Zorin and/or Linux Mint and compare that to a Fedora(-based distro; like Bazzite or Nobara) or an openSUSE Tumbleweed (or perhaps even an Arch(-based distro) if you're feeling brave). If the differences are negligible, then you shouldn't let this be a factor to take into consideration. But if it isn't, then you might want to (at least) consider switching over to a distro with a newer kernel (eventually).

Finally, the 'old' kernel is -in a sense- one of the reasons why both Zorin and Linux Mint are even popularized for newer users. But, that's something I won't be able to go over in this comment for the sake of brevity.