How do you play a game that you bought on a different account without logging into the...

If you're on console, the account that purchased the games would need to set the console as its Home console. https://support.xbox.com/en-US/help/hardware-network/console/my-home-xbox

If you are playing on the same console, no, you shouldn't have to. Try logging in with the account that bought the game, then log in with the account you want to play the game without logging out the account you bought the game with, then try again.

I guess these were bought when I was logged off. And therefore not on my account

What do you mean you bought them while "logged off"?

All purchases you do on Microsoft Services have to be tied to an account. So it might be that you were logged in to a DIFFERENT account.

Since it's not possible to move purchases from one account to another, you will have to sign in with the other account that you used to purchase the game, and download that account to your Xbox console as well.

Then that account can see the games under "My Games", and if necessary, that account can set the console you're mostly playing on as that account's "Home Console", so your other account can play these games on that console as well.

Hey there MidBadBoi!

Check out our
Xbox One Home Setting support page to set your Xbox One console as your home console. This will allow you to play digital content you purchased and installed offline! Hope that helps!

Hey there, Redneckboy! All games will need to be installed onto the Xbox One to be able to be played. This thread is a little old. If you need further assistance, please post up a new thread detailing what you're running into and troubleshooting you've completed.
This way our community can get you the individual support that works best on the forums.