score:5
Although VIE Airport is between Vienna and the Hungarian border, it's not on the main East-West rail line (there are plans to route some long distance trains here in the future once a connecting spur is built). The airport is also not well connected to the main Austria-Hungary rail line by other public transit, hence it's generally faster to backtrack through Vienna when travelling by train.
You do have a few options:
Upvote:2
DB Bahn lists a railjet Train from the airport 13:33 to Wien Hbf. Connecting to a railet bound for Budapest there, you'll arrive in Györ at 15:17.
If wanting to get there quicker, Aerobus seems to be the only Option at that time.
Upvote:2
oszkar.com tends to get new cars listed as the actual date comes closer. (Personally I don't like to do these last minute reservations, but if you're adventurous enough it may be worth to check them again a day before your arrival.)