I cannot use my Apple-login to play on the website

This might mean that you have chosen to login to the app with your Apple-ID but not share the email with us. 

In this case you can follow this guide: 

1: Go into settings and click on your Apple-ID

2. Click on Password & Security

3: Click on Apps using Apple ID

4: Click on GeoGuessr

5: Find your email that you can login with (or send us an email if you wish to change it to something else)