Salahadin

While that link will describe the required document, the one I'm providing will describe the process a US Citizen goes through to legally marry in Thailand.
 
https://th.usembassy.gov/u-s-citizen-services/local-resources-of-u-s-citizens/getting-married-in-thailand/
 
Did you submit the same marriage certificate to USCIS with the I-130 petition, that you are now submitting to NVC?  If you submitted something other than what is described in AstroCanada's link then, I suspect you'll need to withdraw the petition, then get legally and lawfully married where you can and start over.  I do not think a non-Arab can marry a Saudi in Saudi Arabia.  If I'm right, (and she is not Arab) you'll need to travel to a country that DOES allow the two of you to legally marry.

To qualify for a marriage-based visa or green card, you must be legally married and officially recognized by the government in the country in which you were married.  So you need to produce an official record of your marriage from a public office, in this case, Thailand.  A religious certificate would likely not be accepted, hence the rejection.  What's officially recognized in Saudi Arabia may not be recognized by the United States immigration services.

was thinking the same.

The state department will tell you what documents are accepted in their reciprocity tables here:
https://travel.state.gov/content/travel/en/us-visas/Visa-Reciprocity-and-Civil-Documents-by-Country/Thailand.html

Your wife a USC living overseas is required to file US income tax..  Even if she does not owe income tax she is required to file.  Thus you could try Not available with an explanation that she will/is filing back tax returns. 
-EDIT-
 I checked and it appears that she is NOT required to file if she does not have income from any source below a certain threshold... So you should be able to choose not available with an indication as to why not available