Not quite.
They (the consortium in your link) are designing and building only that portion of the track that actually goes into the airport to link the airport from the tracks that skirt the airport. (And the station at Pearson.)
The rail line from Union Station to the Airport utilizes the track right of way owned by GO Transit called "The Weston Subdivision". This is a former CN track that was a singular track leaving Union Station and heading parallel ot the Gardiner, then cutting northwest around Strachan Avenue and crosses King, Queen (at Dufferin), Brock Avenue (north of Queen), Lansdowne (south of Dundas), Bloor (at Perth), Dupont (at Annette) and so on out through Weston towards the airport. It was a very old right of way that CN owned. Over the years, the freight traffic dried up at the south end of the track to 0 and GO Transit became the major operator on the line - at least as it left Union Station, probably up to about the 401 around Carlingview. I think there is some small freight customers for CN up there. (Though GO only leased "running rights" from CN, they did not own the track.) Finally, maybe 10 years ago, maybe 15, I'm not sure, GO bought that portion of the Weston Subdivsion from CN. The Weston Subdivision GO calls its "Georgetown Line" because, wait for it, it runs to Georgetown. (But it's technically known as the Weston Subdivision. Georgetown (I guess) means more to commuters than Weston (which is now a part of Toronto anyway, but used to be its own little town) (GO also bought several other lines running out of Unions Station, but that's another thread.))
GO also bought TTR (Toronto Terminal Railways - which used to be owned by CN and CP jointly and was the owner of the tracks that came out of Union Station.) CN and CP have 0 interest in running or owning Union Station, or passengers as it's only a money pit for them.
Fast forward to when the decision was made to run trains from Union Station to the airport.
The "Weston Subdivision" is the best rail line for the job because it runs out of union station and north west and skirted the airport, then off westwards to Georgetown.
Metrolinx (the parent company I suppose you might say) of GO Transit (all owned by the Provincial Government) decided to build a service to run passengers from Union to Pearson. Originally, it was going to be called "Blue 22" (because the trains were to be blue and the trip was supposed to take 22 minutes) and it was going to be designed, built, operated, AND FINANCED by SNC Lavalin (truth be told, Lavalin would have just been the face behind Blue 22, there would have been a host of players, big and small that owned a far greater interest than Lavalin ever would have). However, the price tag vs. the potential returns didn't add up for Lavalin. (And the reason it didn't add up was because no-one, not even now, can say just how successful this rail link is going to be. Who knows how many people are going to take the damn thing? SNC Lavalin (corrupt bastards that they are) demanded assurances from the provincial government that the province would cover them if their business model didn't pan out. (In other words, the province would be on the hook.) So the province (rightly) told Lavalin to fuck off and that the province through GO Transit (now Metrolinx) would build the damn thing themselves.) The entire thing has now been renamed, "UP Express" I believe, as in Union Pearson Express.
The "air link" to which you are referring to is the final bit of track that spurs off from the Weston Subdivsion and actually goes right into the airport. That is the new concrete bridge you can see when you are entering the airport on the north side of the road leading to Terminal one. It's as cheap of a cheap design as you could get. That is being built by a consortium - Dufferin Construction, aka Holcim, and Aecon (owned by a Swiss bank I believe) and whoever else.
It's not the entire service.
That is Metrolinx (aka GO Transit) and the taxpayers are paying for it.
The Weston Sub had to be upgraded all the way from Union to Pearson. It is being increased from 1 track to 4 tracks. Where there were at grade crossings, now there are grade separations (bridges) and all bridges had to be widened to accommodate the 3 new tracks. The reason is that the Pearson train will need 2 dedicated tracks. One track from the airport and one track to the airport so that UP can run regardless of VIA, or GO, or CN. Nothing can get in the way of UP. The third track is needed for GO, the fourth for a combination of passing, GO, VIA and CN. (Though the trains can all switch from any of the 4 tracks at various turn out locations.)
The biggest bottle neck was "Toronto West Diamond" where the CN (now GO Transit) track (Weston Subdivsion) crossed at grade with the hugely busy CPR tracks (I believe it's the CPR North Toronto Subdivision, but it could be the Galt, I'm not 100 % sure). Freight gets priority over GO. Anyone who rode the GO in would tell you about stoppages at Toronto West Diamond (in the Junction) around Keele and Dundas while they waited in the GO Train for a freight to pass.
Obviously with the train to the airport running several times an hour, the diamond had to go so that the UP express could proceed without delays right from the airport to Union Station.
