I agree it's not a park, but I think it falls short of leisure=sports_center according to the definition on OSM wiki (1st link below).  I've thus outlined the baseball and soccer fields separately with leisure=pitch.  I've also marked them with access=private and website (2nd link below).

https://wiki.openstreetmap.org/wiki/Tag:leisure%3Dsports_centre

https://www.openstreetmap.org/changeset/134625823