Perhaps that could help a few here. We are abord MSC World Europa. Departed Dubai on Jan 14th. We applied for the Saudi Arabia Transit Visa for via https://visa.mofa.gov.sa/ as instructed 2 weeks prior and nothing happened. The cost for us as Canadians turned our to be $ 26.85 taken via 3 distinct credit card payments. I picked the basic insurance package. Our applications were visible on the website right away and remained "Under Process" and in fact are still showing "Under Process" as I'm writing this note despite the fact that we have received our visa by email earlier today during the stop at Sir Bani Yas Island. That is approximatively 48 hours before arriving in Dammam. Interesting fact, we also just got our passport back. We had to give them to the MSC crew during the check-in process.
Useful information.
1) For those who can't find Dammam in the drill down list, there is something called Google that can help you for those kind of things. "Port of Dammam" in Google or Google Maps will return King Abdul Aziz Seaport, Dammam 32211, KSA.
2) In the form, at one point you need to enter your address in KSA and other information. I put my phone number (no + before the country code), and the address of King Abdul Aziz Seaport in the address fields. That worked.
3) For the picture, we have uploaded a low resolution picture, 200x200, in front of a white background. If you have a Mac, you can use the Preview app, open the picture and "Resize" and enter 200x200.
Good luck and Bon voyage.