For a new game, certainly. For a re-release of an old game...I'd guess it could go either way. Sony wouldn't have to relicense in order to print new discs of GT2 and sell them.
Why wouldn't they? Licences aren't granted in perpetuity. If a company has the right to refuse Sony a licence for their intellectual property in new games, as has happened in a few instances with every game they have released since GT3 in Japan, why would anyone think that a company doesn't have any say over how long Sony is allowed to use their intellectual property?
Can Sony similarly reach back into their archive and reprint a bunch of PSX discs of Porsche Challenge and actively sell them? Can the original release of GTR2 be sold on Steam now? Can Sega just upload OutRun Online Arcade back to PSN and XBLA? Hell, Daytona is
the name of a city and Sega still had to hack apart Daytona USA to make a remaster of that in arcades; to say nothing about the sad release history of Crazy Taxi.
Do they need to relicense to sell the same game on a different system?
Almost certainly, because what we're talking about here is nothing like Assetto Corsa (but for the record, they probably did too because console licences in the past
have been different than ones for PC games). We're talking about games that are all over a decade old. A couple of them are approaching two decades old. They predate Playstation Classics, Xbox Originals and even Virtual Console. There's no reason to believe that Sony got manufacturers to agree to licence terms that essentially said "we want to be able to sell this game new 20 years from now as well." And games get removed from digital distribution systems all the time due to licencing problems. Rockstar has very notably had to remove Grand Theft Auto games from the various services several times to edit out licenced music that they couldn't (or wouldn't) continue licencing.
Free money is not to be sneezed at.
If it was actually free money, there would be a lot more classic titles with licenced content on modern digital distribution services. If it was free money, Sony would have had GT1 or GT2 be the very first games on the program as soon as they started the Playstation Classics line instead of Hot Shots Golf 2; if for no other reason than to fill the huge hole left by GTPSP's ridiculous delays. I'm looking over the Playstation Classics list, and I see maybe 8 games that notably had licenced content in them. Most of those are Rockstar games. There are games that were absolutely humongous when they were new on the system from big publishers that are nowhere to be seen, and would almost certainly sell well if they were announced. There is only one Need for Speed game. There are
no Tony Hawk games, or any of the titles in the same spirit. All of the licenced tie in games are ones that the licence holder had a hand in publishing themselves. In fact, the highest profile racing game in the entire PSX catalog seems to be R4; which isn't a knock on that game but it's rather conspicuously a game exlusively featuring content Namco produced themselves.
I think it's very unlikely that Sony is deliberately not rereleasing a humongously popular first party game on the digital distribution system they control, especially when the sequels in that series are infamously slow to release, if it was easy for them to do so. But it's completely ridiculous to assume that all of the third party publishers (except for Rockstar) who made their biggest marks on the industry with games they released on the PSX and PS2 are similarly willingly leaving money on the table if it was so easy to get.