The land of the former amusement park has been given to the Budapest ZOO after the amusement park closed at the end of the 2013 season. Most of the amusement rides were removed back then, with only the protected structures such as Hullamvasut, Merry-go-Round and a small dark ride left operating.
At the end of 2015 the amusement area of the park closed to be fully integrated into the aformentioned zoo as a new area called Pannon Park. The concept of the new area seems very ambitious and I believe money has been a bit of a problem, since the opening date of Pannon Park keeps getting pushed to a later date (at the moment the website says it should open in the Winter of 2020/21)...
Relevant bit of the website (if you use Google translate/speak Hungarian somehow, there's a lot of interesting info elsewhere on the zoo's website):
Állatkert Budapest szívében
zoobudapest.com