If I buy a Xbox 360 game on the Microsoft Store, will I be able to play it on my 360 console?

I'm not sure if there is a difference in those listings as a 360 game should work on the 360. But you can use Paypal to make purchases on the 360 store.

I tried yesterday, but couldn’t find the PayPal option on the 360 store.

I think it’s unavailable in my country

Battleblock Theatre is an Xbox 360 game. It doesn't matter if you get it from the Microsoft Store, The Xbox 360 marketplace website or the console. You will still be able to play the game on the Xbox 360.

I have to agree. My Xbox 360 recently broke, and instead of having to buy a 360 and Xbox One, I would like to still be able to play the old 360 games on the new console. Yes, I know it's not possible due to the completely revamped architecture, but they
could still offer 360 games digitally through the games store couldn't they?

Besides, Microsoft said that they are still ironing out Backward Compatibility, and that it could still happen. Just gotta keep your fingers crossed.

Hey Mr Anarchy4Dayz,

Welcome to the Xbox Community, great to have you!

You are able to buy older Xbox 360 games on disc and you'll be able to play them on Xbox One if they become compatible.

You can also buy compatible Xbox 360 games on the Xbox One store via your console.

Hope that helps!