No it doesn’t. The price parity thing is only if you are selling the game on Steam platform, i.e. selling a steam key, it’s essentially a way to allow publishers to sell the game on their own website, without paying the 30% to steam, but don’t allow them to undercut steam entirely while still taking advantage of their platform.
Games on GoG, itch, Epic store, etc, can have any price they want, as long as they don’t give away a steam key valve doesn’t care what price you sell your game elsewhere.
This is one of the most annoying fake news out there, Valve are going above and beyond what any other store is doing, and they get bad rep from people who have never read their policy, published a game there, or talked to anyone who has.