The Beer Store/LCBO are Ontario Government , at least at arms length, are they not?
I had difficulty getting my Ontario Driver's Licence using my Military ID, when I moved from Manitoba. You need 1) your other province's DL - check; 2) proof of citizenship/residency - my Birth certificate (in maiden name, though) - check; 3) and proof that you are who you say you are, if the names on the first two are different. I didn't have a passport at the time (expired). My military ID, with photo and signature was not sufficient. I tried to explain that a permanent military ID is as good a piece of ID as a passport or citizenship card to prove my identity, no dice. They would have accepted an Ontario government employee ID, but not a military ID. The only other acceptable way of proving my identity was with my marriage certificate. OK, so I came back with my marriage certificate. Unfortunately, I have only ever had the one issued by the church, not the official provincial one, and the church one wasn't good enough. (In 15 years of marriage, the Ontario government was the only organization that didn't accept it as proof of name change, BTW). So I had to order an official marriage certificate from Manitoba, wait for that to come in.
In the meantime, I went on the MTO website and wrote a (very polite) suggestion in their "ask a question, feedback" section that they consider military ID as a valid proof of identity, in addition to passports, citizenship cards, and Ontario Gov't employee ID. Included my contact information and asked someone to get back to me. Never heard a word from them.
Most places - "Government Issued Photo ID" is the norm. Why is a military ID not automatically on that list in Ontario?