I tried to provoke this.
I closed my browser, Opened four different private browsers. Pointed them to https://itch.io/games and tried to press enter on all of them in the same second. I managed to get a 429 in the first browser.
Closing the browsers, trying again. No error. Closing the browsers, trying again, again no error. Browsing a bit, setting it up again. This time the second browser got a 429. Then I tried to spam reload button. No errors. Then I opened here again to write comment and got 429. While writing I opened another private browser to search if I actually used the correct reload button (i used ctrl-f5). Then I opened https://itch.io/games again, and got a 429 first time. I then spammed the other reload button (shift-f5) and all were served without error.
Conclusion: No clue. I can't remember to have gotten this error when opening a huge amount of background tabs with games. But only on first tries - with and without login cookies.
I also tried as a final test to open the browse page in new private window, and immediatly closed it, when not getting a quick answer. Maybe every fourth try resulted in a 429. Sometimes consecutive, sometimes not.
So my best guess is, that itch is suffering a ddos attack or some component is overloaded with regular accesses, like maybe the login server.