The question "Can the Android version of the games downloaded here be run directly on the phone?

It depends.

By default, Android devices come locked and do not allow you to install applications from stores that Google or the manufacturer does not want, so no, you cannot go and install an application from Itch.

If you use Itch or another store, you will normally have to enable the installation of "unknown" applications (that's what Google calls the

option), in which case, it may still happen that the APK comes compressed in a . ZIP and in that case, you must unzip the . ZIP before you can install the application.