Is abandoning prayer for four years due to daily masturbation and parents preventing frequent ghusl considered an intentional abandonment of prayer that does not require making up, or is this considered an excuse that necessitates making up the prayers?

Abandoning a single prescribed prayer until its time expires is a grave sin, greater than adultery, theft, consuming alcohol, and murder. What you mentioned is not an excuse that permits abandoning prayer. Rather, it was obligatory for you to perform ghusl. You have committed a sin and neglected your duty by intentionally abandoning the prayers. You must repent to Allah with sincere repentance. Part of the completeness of repentance, according to the majority of scholars, is to make up those prayers, which is the more cautious approach and better for absolving oneself.