The ICE (InterCityExpress) takes around 1 hour 50 minutes, so I don't understand why there are also planes from Austrian Airlines serving this connection...
Austrian Airlines do have flights from Vienna to Linz - their schedule advertises the duration as 40 minutes. Add Travel to/from the Airport, check-in time etc, and it would be well over the time taken by the train.
What the original post probably means is that the Airline and Railway have agreed to a Codeshare deal, where the trip takes place on the train.
Similar deals already exist in Germany with Lufthansa and Deutsche Bahn. If you try the Lufthansa Website and try to book a ticket from Sydney to Cologne, you will find that one of the options for the last sector - Frankfurt to Cologne - is Lufthansa "Flight" LH3606 (the number varies depending on the time of day) - actually a Train Service operated by DB, for which Lufthansa book a number of seats.
Edit - sorry, I just realised that the Original Post was 5 months old, but resurrected today.