There are tons of different games. All of them do not necessarily become famous. But most of these games have something unique in them.

I disagree. Most games have a unique-ish combination of non-unique features. Those unique combinations can be used as selling points.

Marketing may call something a unique selling points for a specific genre of game, or because it merely does that feature better than prior existing examples.

Bioshock's USP is that it's set underwater.

So prior to Bioshock, no game took place primarily underwater?

Bioshock Infinite's USP is that it's set up above in the sky.

So prior to Bioshock Infinite, no game took place primarily in the sky?

The story cannot be its USP either because the story is something that you experience as you play the game and not before you have actually bought it

"You're Gordon Freeman, a new scientist at Black Mesa. Everything is okay until an experiment goes horribly wrong! Can you stop an alien invasion and save the world?"

This is a selling point. It's unique-ish (at the time of release) because few games had you playing a scientist. Most were burly herculean figures.

My argument is that I think it's not necessary for a game to have a USP for it to be famous.

Agreed.

Call of Duty and Battlefield do not differ from one another but are equally famous.

Strongly disagree. Poor example.

Battlefield USP compared to Call of Duty:
- Humongously open environments
- Vehicular combat
- Large scale battles (BF2 = 64 simultaneously)

Modern Warfare USP:
- Focus on player customization and unique loadouts
- Leveling up and unlocking new gear
- (and superior graphics, but maybe you don't count that)

Temple Run and Subway Surfers aren't different either but are equally famous.

I've heard of Temple Run. I've never ever heard of Subway Surfers.
I've played neither, but Temple Run is famous enough that I've heard of it despite having never played it.

Taking a mechanic from one game and adding it with a different mechanic of another game doesn't make it its USP.

Yes it does.

Something that's common place in one genre might be a major selling point in another genre.

Neither does altering that mechanic make it its USP.

Yes it does.

Mechanics are frequently tweaked and expanded and improved, and these improvements are often used by marketing as selling points for the game.

My friend thinks that every game has a USP unless they are AAA companies in which case they don't need a USP for the game to become famous.

Very few games are exactly mechanically identical. Marketing exists to sell games by hyping what makes them unique, even if it's not actually unique.

Smaller studios have to compete on gameplay, because AAA quality graphics is more difficult (but not impossible) for them to reach.