The NHL gives very little to teams in terms of details around contracts unless prompted. There is a database that teams can access or link to that has basic stuff like years/AAV/etc. A lot of details are not fully available, though some are. Teams can also simply ask the league office for any data, but that's pretty much a last resort. A clear instance of this is Dadonov... he had a NTC. The NTC was known by Vegas, but Vegas was under the impression that one was not filed and thus the NTC was void for that year. When the truth was that it was filed by Ottawa and they didn't disclose the details to the Vegas... which they were required to do. The NHL basically keeps that communication between teams, or tries to. Which bonuses exist, salary in a given year, which clauses exist, etc. All those details are the trick.
What CF had was an easy database teams could access with that data. Bettman is famous for shitting on these sites saying they aren't confirmed data... but CF had it pretty close (like 98%). Which signing bonuses exists, who's contract is thus buyout proof, what the NMC/NTC clauses are, what ELC bonuses exist, etc etc. That's what teams paid for (and the UI... where the NHLs is basically an Access database). Somebody else to track all that data and give them a nice, clean API without having to have a staff member do it. There is something like 1300-1400 contracts in any given season, so there is a good amount to track... and teams are naturally cheap.