Did you misread the highlighted browse? That was not the verb for using your browser. That was a reference to the feature right next to the itch icon. It is called Browse.
Browsing for direct links elsewhere is not the issue. The issue is, that you can get those direct links with itch's browse feature, without opted in. The correct behaviour would be to display nothing or a page that you need an account and not just show the goods. (In the case that all games tagged adult would be marked adult. I can not verify that. But I doubt that it is congruent, as the "sex" tag example showed.)