Can I install a new 30A breaker in an empty slot in 125A panel?
The first page of the manual indicates a CSA listing, which due to treaty bears the same weight as UL.  So you have to follow the instructions.  The listing is contingent on doing what the instructions say.  

So yes, a 10/2 cable with 30A (greater than 25) breaker to a solitary single NEMA 5-20 socket, labeled for this one appliance, is what's called for.  This is a special socket that should not be used for any other appliance, unless that other appliance also specifies a "greater than 25A" breaker.   

If you want to also support other circuits, then throw in a 10/3 and install a subpanel. Bonus points if it's a GFCI hot tub panel, because that will answer the GFCI requirements on any garage circuit.  Preferably a GE type that supports their weird 1/2" breakers because then you can use "double stuff" breakers for density and still customize the breaker size for each load.  

By the way, you can't ordinarily bump breaker sizes in response to nuisance tripping.  You can do it here, because of a special motor rule, and because the instructions said so because of the special motor rule.