No, that's not required. Microsoft was hit with antitrust despite users being able to install alternative browsers and even operating systems. The problem was that Microsoft was being anti-competitive by making competition more difficult, not that competition wasn't allowed.

You can certainly get a DP-to-HDMI adapter if you want, but that doesn't mean there's no anti-trust happening. If a new TV manufacturer can't reasonably enter the market due to the protocol being overly restrictive for most accessories, I can see that being grounds for an anti-trust case. If they want HDMI to be a standard, it needs to be open. If they don't, they need to provide alternatives in their products.