By visiting the website, you're the one pulling, wanting to visit and viewing the content or messages on your time. By installing the app, any message or update is pushed to you instantly, pulling you to the website, making it less your decision to visit, but being pulled in. A Medusa-like call that's hard for many to resist.
Reddit are not unique in this. Even updated 'XXX sent you a new DM' from Twitter via email for example.
Anyway, I'm shot of Reddit. Their recent purge shut down a lot of subs that for many were mutual support groups caught in the cross-fire of admins vs. sophisticated trolls using them as flare-scatter to escape themselves.