I still buy music on CDs and I've no desire to get a Steam account or something similar. Is it still possible to buy games on physical media? Do you then need an account of some kind anyway?

On consoles, absolutely, it's a fairly rare occurrence for console games to only be released digitally. On PC... it's becoming very common that, even if you buy a game on disk, you then have to 'validate' the install by logging it into Steam or Origin (if it's an EA game) or Battle.Net (if it's a Blizzard game). You pretty much can't play those games unless you have an account on the relevant service. But you don't need to download the game through that service, so there's no reason to give them credit card details for example.

So I can't really game without an account of some sort either way then. Gay.

Well I can't really game on my hardware anyway, with anything recent at least. So I guess I'll be waiting...

Minesweeper.

Go for older games, which will be dirt cheap on eBay.

If it's backing up and DRM you're worried about, it might be worth checking out GoG. You need an account to buy stuff (of course), but there's no client software you need to install to play. Downloads are supplied by way of an installer EXE, so you can burn that to a CD/copy it to a pendrive/whatever and keep your own hard copies. Not as aesthetically pleasing as a shelf full of cased games, but adequate for making sure you'll always have them.

It does have optional client software, but AFAIK that is basically a download manager and nothing more. I've bought about 4 games from them and never used it.

Well today I installed Arma II Free and now I don't want to play anything else!

I just wanna buy a joystick and throttle and start hitting hot LZs with a chopper full of my mates! Oh dear....