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That is an interesting question. Most of my games are in digital format so I am fully aware that I "own nothing". And I somehow doubt that by having a DVD or CD of something, I might be entitled to it either. Public domain is another topic we should address. Also, copyright will never represent consumers, just the content creators and the publishers which earn the real money here. What's in our best interest is out of the question. Take licensing for example. So many excellent games are forever gone from fully legal storefronts and that practice only encourages piracy.

Speaking of Ubisoft.
https://youtu.be/RTkxzQDo0ng?t=1

You own the medium it's on, but the code is not yours. The license agreement also often forbids you from modifying the code in any way, and bypassing copy protections may or may not be legal where you live. So basically, you own the disc itself, but what's on the disk is not entirely yours.

It's basically the same as owning a music CD. You own the disc, have a right to put it on a device and play it at any time, but you never own the content.

What's the real point in owning physical copies of games if you have to download content for them to run, unless you get them cheaper? I can understand with single-player games that don't require a server, but online multiplayer games... That's the question I'd like to understand.

That's a problem with things like Spyro Trilogy on Switch not having all 3 games on the cartridge. When the servers shut down in the future you will no longer have access to the full Trilogy because required download is unavailable.

You actually get a lot of console games that you can just install and play if you own it physically, I'm not sure about FarCry Primal but I can verify that Horizon Zero Dawn, God Of War, Rise of the Tomb Raider, The Order 1887, Infamous Second Son and a few other games work without needing any internet connection to download an update or authenticate anything.

It's a rent. And in some cases, a rent you're only allowed to make use of if you also agree to abusive EULAs like allowing the publisher to spy on your whole computer (hurray for multiplayer games)

Short answer: no, buying it just gives you the right to play it. That's it.

Owning a copy in theory gives you the rights to give or sell that copy. So yes, you own the copy, you just don't own the game. It's an interesting distinction. Owning a physical game doesn't guarantee that you'll be able to play it in the future. If it's an offline game and you have the exact hardware it was designed for, there's a good chance you'll be able to run it. Otherwise, it's a matter of luck.

In general, everything that's under copyright, you only get to own the copy, not the content. You aren't allowed to make another copy of that content, nor are you given a license to other forms of that content. With digital, because there's nothing there to really own (digital copies are trivial), you don't really get to own anything. But with physical, all you get to own is the box and the disc, not the game itself.