TLOU2 is a full exclusive, which means is only available on a console brand.
Street Fighter V is a console exclusive, which means it's only available on a single console brand and on PC.
Deathloop is a timed console exclusive, which means that at launch is only available in a single console brand and some months/years later may/will be released on other console brands.
Nobody uses 'omni'.
The previous Kojima game was a Sony 2nd party game, which means it was published and funded by Sony, did use a Sony engine, got a 84 MC and was profitable.
Later, even if Sony owns the IP, Sony let them port it PC with another publisher, that port was also was profitable (very likely Sony also got part of the PC port money).
So Sony and Kojima had a good relationship before Death Stranding, and both very likely are happy with Death Stranding. So despite what rumors may say, it's very likely that they will continue working together.
Even if Kojima decides to keep or himself the IP of the next game and wants to self publish, Sony can support it as a timed 3rd party exclusive as Sony is doing with many 3rd party both AAA and indie exclusives, or even if Kojima wants to go full multiplatform since day one Sony can support him with a marketing deal as did with many 3rd party AAA and big indies before.
They recently announced Virtua Fighter 5: Ultimate Showdown, an anime space opera-like Strategy RPG with mechas from Kadokawa as 3rd party Japanese exclusives, and it's rumored they will announce a Final Fantasy spin-off from Team Ninja plus they will soon have Guilty Gear Strive and Square JRPG stuff with Final Fantasy and a new AAA IP. So they are going strong betting on Japanese 3rd party exclusives, and now from Sony XDEV pretty likely they will do a better job with future 2nd Japanese party games.
I don't see why Sony or Kojima wouldn't want to continue working together in the future, specially now in Sony's side that they downsized Japan Studio, so they will release less stuff. It wouldn't be for money, because Kojima went with Sony when any big publisher would have given Kojima a blank check to go with them.
I think they are including 2nd party games in this number as long as they are getting first party help from internal studios like XDev or ICE Team.