It does not work on mobile. When you visit invite (as new user would), e.g. here https://discord.com/invite/trbteNj it will automatically open play store with discord app. It cannot be disabled.

Additionally, when you visit discord.com shortly there is login button visible but then it disappears and only install app button is visible, login is no longer possible.

(It is possible that old users have some cookie settings that allows them to use mobile website but new users can't)

Tested in chrome in Android 10