It is not about mobile access. I use Itch.io App on a PC.
When game is downloadable, or at least compatible with Itch.io App, it is also playable through Itch.io App with no need to login to Itch.io though a browser. This makes accessing the game a lot faster and easier. If the game is downloadable, it allows an offline access, and it when using the App, notifies automatically when a new update was been uploaded. This makes following the games easier and draws an instant attentions to newly added material.
It is ok not have those features, but for someone with over 400 games on the list, it is really time taking to individually hunt down games just in case to see whether there is an update or not. I'm pretty sure there are games I haven't checked on ages, because they "run under the radar".
I suppose it is just a case of personal preference and convenience.