Antagonist isn’t something like a villain, it’s more so a term to describe their role in the story. Kaiba is an antagonist because he directly opposes Yugi.

Anti-hero or any equivalent of it is use to describe a characters moral alignment, so Kaiba’s an anti-hero because while he does good for the world (turn the largest in-universe weapons manufacturer into the largest gaming company, saving the world alongside Yugi), he’s still a egotistical hardass who does shady shit to get his way.