Is it required for a woman to squirt, in order to have an orgasm?

NO. “Squirting” is controversial. Some indicate that it is a form of female ejaculation in which the fluid is propelled from para-urethral ducts during or prior to orgasm. Others hold that it is lubricating secretions or incontinence of urine.
Female Sexuality. Please get a hold of a sex manual or one of the female anatomy and sexuality guides. I often recommend to my female friends and patients "our bodies our selves" or "the joy of sex" so that they can be informed about their own bodies and sexual functions. An orgasm for a female is a nerve reaction not a squirting. It is stimulated with stimulation of the clitoris.