If you're just looking at browsers, then how about Microsoft, which still has a dominant browser market share.
If we're looking at desktop operating systems, Apple and Microsoft are the main suppliers. They provide built-in support for H.264, not WebM or Theora.
However, when looking at content providers, Apple is a very important player. The majority of online video content is sold through the iTunes Store. And rental places like Netflix and Hulu also rely on H.264.
It’s not really sensible to only look at browsers (and, presumably, only desktop browsers – Apple has more than 6% market share of mobile devices). Which formats do digital cameras use? Which formats is content sold in?
And these are? No, Apple is not one of "the most important players in the industry". Safari has only some 6% market share.