Shouldn't I be able to play my paid for downloaded games without network, on or offline?

You can play offline unless it's a game that's online only. https://support.xbox.com/en-US/help/hardware-network/connect-network/using-xbox-one-offline

Just found this 'The game was removed from the PlayStation Network in October 2010, with the Xbox Live Arcade version being scheduled for removal in December 2011.' But seeing that I paid for it, shouldn't I be able to download it again?

The game is free to play as you haven't paid anything to buy the game. It still uses all the same network infrastructure as any other game on Xbox live so the cost shouldn't be paid by everyone else so those that want to play for free can.

Just my opinion.

Hey. So I imagine you all know that Xbox is down at the moment. I have the day off and wanted to play something. I bought all of my games digitally and now it's asking me if I own the game or app... Now I specifically remember Xbox stating that they were
getting rid of DRM but now it seems that it's still there. Why aren't my games working? I paid for them and would assume that I should be able to play them on my console. It shouldn't matter if there's a problem on their end since I put money into the games
and should be able to at least play them in offline mode or something like that. I'm seriously about to just quit console gaming over this, since I paid money and am not getting what I paid for. Please help.

I shouldn't have to invest my time into something just to "fix" my reputation. That's like putting a band-aid on a broken system. I just want to be able to play the game that I paid good money for and my reputation shouldn't be governed by players from a
competitive game. They block you just so they don't have to play against you again.