Sadly yes, popular sites get copied a lot, so the safest habit is to bookmark itch.io and open games from there instead of from search results. You said you almost got caught, but if you did run anything from that site, it's worth checking that it didn't leave something behind. On Windows, open Windows Security, go to Virus & threat protection, then Manage settings, and under Exclusions click Add or remove exclusions. Remove anything there that you didn't add yourself.
After that, run a Microsoft Defender Offline scan from Scan options, since it restarts the PC and scans before Windows fully loads. If you typed any passwords while that program was on your PC, changing them from another device is a good idea too. Glad you noticed before it got worse.