Relative to the location of baptism outside of a parish, Archbishop Apuron has decreed thus:
Outside the case of necessity, it is not lawful for one to confer the sacrament outside of his own parish without the proper permission. - III. A. The Sacrament of Baptism, Handbook of Faculties - Archdiocese of Agana, Archbishop Anthony S. Apuron, December 22, 2006
The handbook references the relevant section of Canon Law which reads:
Can. 857 §1. Apart from a case of necessity, the proper place of baptism is a church or oratory.
§2. As a rule an adult is to be baptized in his or her parish church and an infant in the parish church of the parents unless a just cause suggests otherwise.
Can. 860 §1. Apart from a case of necessity, baptism is not to be conferred in private houses, unless the local ordinary has permitted it for a grave cause.
§2. Except in a case of necessity or for some other compelling pastoral reason, baptism is not to be celebrated in hospitals unless the diocesan bishop has established otherwise.
So apparently, Archbishop Apuron is permitting all these gymnasium baptisms "for a grave cause" (Can. 860 §1.)
Relative to the recordation of the baptism, church law requires thus:
Can. 877 §1. The pastor of the place where the baptism is celebrated must carefully and without any delay record in the baptismal register the names of the baptized, with mention made of the minister, parents, sponsors, witnesses, if any, the place and date of the conferral of the baptism, and the date and place of birth.
No exception is given in the law for the recording of the baptism. It must be recorded by the pastor of the place where the baptism is celebrated. The Bishop Baumgartner gymnasium is in the parish of St. Jude. The baptism must be recorded by "the pastor of the place".
But then Catholic Church law only applies to Catholics, so no worries for Archbishop Apuron and the neos over at the gym.