This reliable spanish site I go to, http://www.speksnk.com, says that Playmore is the new SNK, posesses all the licenses to SNK's stuff.
Es la nueva SNK del futuro, ya que posee todas las licencias de juegos, maquinas, y todo lo relacionado con SNK & Neo Geo.
Basically, it owns all of SNK's old stuff.
Eolith apparently has the rights to KOF2k1 and KOF2k2 by way of a collaboration with Playmore... i.e., Eolith gets KOF2k1=2k2, Playmore gets the rest, or can opt to allow Eolith to develop the rest of the KOFs.
That's where I got all that info from. It's in spanish, tho. A translator should do it, as long as you don't mind Daravonese.
What proof do they have?
This site, to put it bluntly, kicks ass. It's purrrrrrrrrrty. Of course, I don't know any japanese beyond Shun Goku Satsu, so I can't confirm it. But, that "OFFICIAL NEO GEO SITE" logo up in the corner seems promising.