Here are two really good links (particularly the second one) that may help explain 23andme's weird reporting system as it relates to the more common DQ type nomenclature:
http://www.ncbi.nlm....es/PMC2386975/#!po=53.1250 – This is actually a study. Very informative and interesting if you choose to read through the whole thing. However, if you skip to page 10 and click on table 3, you'll find a list of the celiac related DQ types, their SNP tags as well as risk alleles. I'm not sure if 23andme is still testing for all of these SNP tags, but the DQ2.2, DQ2.5 and DQ8 tags still work for me (my chip is from last September/October). I suggest referencing the first link for DQ2.2, because I think they've since updated one of the tags.
As others have said, 23andme only looks for DQ2.5 when establishing celiac disease risk, however they are also reporting on a few other SNP's (from different chromosomes or different parts of chromosomes, so non HLA-DQ types) that may be associated with celiac. Their studies and any they cite on these other genes/risk factors have yet to be validated.