Hello, madeinspain.
Thank you for using Apple Support Communities.
Currently, the only method to search for games in Apple Arcade can be found here: Play games with Apple Arcade
"Find games
After you subscribe to Apple Arcade, you can download any Apple Arcade game for no additional charge:
- On your iPhone, iPad, or iPod touch: Open the App Store, and go to the Arcade tab at the bottom of the screen.
- On your Apple TV: Open the Arcade app, or open the App Store, and go to the Arcade tab at the top of the screen.
- On your Mac: Open the App Store, and go to the Arcade tab in the sidebar.
You can also search the App Store for a specific game."
If you'd like to see a specific feature in iOS, submit feedback using this link: Product Feedback - Apple
Cheers!