Well its got the Star Alliance Gold logo above the reception desk so indeed those pax will be eligible for the partner airlines and the lounge looks a lot better than the other options. By March non-Schengen flights will get a boost with BEG, OTP and SOF up to four extra flights per day.
Who knows the arrangement's they've got. I'd imagine BUD are falling over themselves now they've got a legacy back. The lounge might even have been paid for by the airport. The Hungarian political elite were probably not very happy with a legacy third party lounge they had to use. I'll try to find out.
That guide is useless, not even super-hub SZY's cupboard lounge is listed

.