How does "infringed on the Tetris Company's copyrights by replicating elements such as the playfield dimensions and the shapes of the blocks" fall under protecting the brand?
The thing is that they don't have copyrights on playfield dimensions and the shapes of the blocks, since those are actually functional elements of the game. However, they have been able to protect their brand by claiming that these things fall under trade dress.
What they've argued in court is like Ford saying that Chevy infringed on their trade dress by also using wheels, an engine, a steering wheel, etc.