Nope, I dont have to see a screenshot. You cant fix your issues without reinstalling anyway and that means re-downloading.
You need those registery keys, not only to play but also to patch and what not.
BTW, this is not retail, this is a digital version
I noticed though they no longer provide Arma 2 & Arma 2: OA for new customers so I hope they still let original customers download their bought versions.