Here's the guy's LinkedIn page: https://www.linkedin.com/in/dan-fallows-23937124/
Without getting into the legal or contractual aspects, the guy is an F1 aero engineer through and through. He started out at Lola, then Jaguar, then Dallara then to Red Bull. His whole career is in race car aerodynamics.
So, being canned from the F1 team and being required to work on road cars would be a complete change in industry and counter to his career path. If he wasn't interested in doing that, from a pragmatic or 'moral' perspective it's highly dubious for Red Bull to try to prevent him going elsewhere. He's an F1 engineer, he signed up for an F1 engineering role, the company then prohibited him from working on F1 internally, and is now going to court to prohibit him from working on F1 full stop until mid 2023. What?