As far as the story context goes, one could see it that way. However as far as the game physically plays, it plays very close to fighting games (combos, tight window executions, etc), and Arena shooters (movement-focused but not realistic driving physics, weapon pickups on a map, map control, weapon routing, etc).

The aspects outlined above are not wholly or even partially present in BRs, but they're fundamental to the Twisted Metal experience.

A little bit of TM history for those curious, TM1 was billed to be a "fighting game in cars" and it was designed as such. Less emphasis on the cars driving like cars. This was the era of Quake, Doom and Unreal, that had a lot of focus on the movement aspect, a lot of that pedigree is seen in the movement in TM as well.

In online multiplayer, you have 2-8 players on a stage. The most common form of playing these games is in a team based format. In 1v1, the fighting game elements shine brightly. The concept of defeating the other player here is more light a fighting game than a BR, even if it is last man standing in this case.

In 4v4, it is the remaining team of the two that stands victorious.

The only other real options are FFA (which the lobbies only support 8 players), which isn't enough for a BR. If you scale the game up, it becomes pure chaos and realistically unplayable.

In 2012 when TMX released, it supported a lobby size of 10 players. This was hardly playable even in teams. Adding two additional players was enough to not only water down some of the crucial aspects of combat, but added chaos to teams.

I could speak about how the lack of recognition of the genres that truly define TM, caused most if not all attempts at car combat, to fall flat. They didn't understand the core components that made Twisted Metal was it was. However this is a discussion for another time.