I didn't really recommend Opera. Any closed code has less potential for audit. That's a built in drawback. With browsers you at least have choices.
And as for the DRM aspect, when a game with Steam DRM implemented runs, all it does is check to make sure Steam is running and that you're authorized to run it.
You hardly can guarantee what DRM does or does not, because the same DRM isn't open either. You assume that's what it does. Assumptions aren't enough when it comes to issues of trust and security. And by its mere definition DRM can never be trusted - ever. Simply because DRM itself never trusts the user by its own definition (that's the point of DRM - to consider user a potential criminal), and trust is a mutual relation, so DRM can always be viewed as a potential threat in return.