You purchased the game for offline yes I agree, but the Beta was only ever available online. If offline was all you were ever interested in, then you should have told FD that you only wanted to test the offline Beta as soon as you found out that offline wasn't part of the Beta testing. At that point I think you would have been entitled to a refund for the Beta too. But you didn't do that. You continued to play/test the online Beta until you found out that you weren't going to get an offline game at the end, then you wanted a refund for both the Beta testing (which you'd already had access to), as well as the final game.
If you had no interest in playing/testing the online Beta, then presumably you wouldn't have accessed the online Beta until an offline version was ready to test.
Whether you were helping FD test the online Beta isn't relevant I think. Everyone who had access to Alpha, Premium Beta, or Beta payed to help, otherwise we'd be professional testers, and would be spending most of our time trying to systematically repeat scenarios that replicate bugs, in the interests of nailing down the definite cause. I suspect what most (if not all) of us have really been doing is playing.