Does celibacy have to include masturbation?

Masturbation does not make you not-celibate

Sex with someone else does

Celibacy means to refrain from sex with other people. However in the cloisters where people are expected to be celibate for reasons of faith masturbation is generally also discouraged. 

What is the point of celibacy if you masturbate?

Celibate means to abstain from all forms of sex including masturbation. In pastimes priests that were going to dedicate their life to God and remain celibate would have their testicles removed or crushed ouch they were then called eunuchs.