Not quite, but close. An arbitral tribunal (like the CAS) isn’t a “real” court, in the sense of being a government institution. And so while arbitral awards are generally binding, if there is a fundamental flaw in the arbitration process, you can apply to vacate the arbitration award. The grounds for doing so are very narrow, but this appears to be what they intend to do, given their reference to the Swiss courts.
Yeah, to be honest, it’s a long shot. But worth it just to make them spend more time, money, and reputational capital defending the indefensible.