As quoted from the linked post.
It looks like you’re part of one of our experiments. The logged-in mobile web experience is currently unavailable for a portion of users. To access the site you can log on via desktop, the mobile apps, or wait for the experiment to conclude.
This is separate from the API issue. This will actually BLOCK you from even viewing reddit on your phone without using the official app.
Archive.org link in case the post is removed.
https://web.archive.org/save/https%3A%2F%2Fold.reddit.com%2Fr%2Fhelp%2Fcomments%2F135tly1%2Fhelpdid_reddit_just_destroy_mobile_browser_access%2Fjim40zg%2F
I don't think they ever confirmed it, but I'm pretty sure for a while they were experimenting with blocking people who used VPNs too. There was about two weeks where reddit just didn't work on my laptop and I couldn't figure out why, until I saw a thread where other people were discussing it and someone said try it without the VPN. Sure enough, that did it. Then after a couple of weeks it went back to normal again.
Weird. But blocking people from using VPNs may be a genuine attempt at fighting spam. However if they do it in secret, then it's questionable.
They can spam more efficiently via API calls vs using their web browser/app.