The other major complication here is that Matt has thoroughly mixed his several roles together, so you have to spend time untangling what is Matt-personally, what is Matt-as-his-company, and what is WordPress-via-Matt. When you untangle that, the core demand appears to be that Matt (in who knows what role) demanded that WP Engine compensate Matt-the-company for its use of WordPress-via-Matt resources being provided by Matt-personally (that no one knew was being provided by Matt-personally as opposed to WordPress-via-Matt). Given the thoroughly tangled mess of that stuff, and the fact that--in the past--Matt made several steps to untangle the ownership of everything, I am not particularly persuaded by the logic of "I'm just trying to get them to pay their fair share," as they're not being asked to pay the people they should be paying.
> why is Matt / WP Foundation acting unfairly by asking for payment?
Because they're asking someone to pay, not the foundation whose resources they are allegedly using, but their largest competitor (a very distinct legal entity).
[1] There are licenses that do have clauses that let you take action, but generally having such a clause makes it not Open Source-compliant, and frequently the relicensing needed to bring the current licenses to that state involves a lot of drama.