I know it's late, but if you click on the sign in through steam button, Steam explains how this sign in works;
- Your Steam login credentials will not be shared.
- A unique numeric identifier will be shared with thingonitsown.itch.io. Through this, thingonitsown.itch.io will be able to identify your Steam community profile and access information about your Steam account according to your Profile Privacy Settings.
- Any information on your Steam Profile page that is set to be publicly viewable may be accessed by thingonitsown.itch.io.
That should help alleviate any fears of your info getting compromised. Also I enabled 2FA several years ago. The only way to log into my account is through the app on my personal cell phone. That all but eliminates risk of unauthorized logins.