score:5
Oman made a number of changes to their visa policy in March 2018, shortly before the opening of the new airport in Muscat in April.
I was there a few weeks after that, and was told that they are no longer issuing transit visas. That said, I can not find an official statement to this fact.
They also now require all visitors to apply for a visa in advance using their online system, and as you said this does not currently allow applying for a transit visa.
I suspect the page you have linked to is no longer current - certainly there are a number of other pages on the Royal Oman Police website that are out of date, broken, or "under construction".
If you do decide to apply for a tourist visa the process is simple, and in my case the visa was approved almost immediately (6 minutes!)
Upvote:3
As @Doc said, the rules changed recently for tourists in Oman.
As a French national, not resident in GCC country (the Gulf), I could see multiple unsponsored visas I could apply for and among them:
One can apply for them online.