Overwatch has a lot of the same sci-fi elements, but I don't think cyberpunk would be an accurate way to describe it. In a way, it's a patchwork of a bunch of different stuff; for example, you might say Sombra is cyberpunk. But I don't think it generalizes well.

One of the main things in cyberpunk (and in a lot of punk genres) is economic inequality and the flaws of capitalism. In Overwatch, large corporations are part of the setting (and so is poverty, I would guess), but that's all they are — background set pieces.