While lots of people, for lots of reasons, are single, celibacy is the willed state of not marrying. [Fr. James] Martin, for example, is not simply single, he is celibate because he chose, as a cleric (1983 CIC1087) and as a religious (1983 CIC 1089), to be bound by two impediments against marriage and to share thereby in the “special gift of God” (1983 CIC 277 § 1) that celibacy is. Other impediments whereby one is prevented from marrying can arise not by one’s personal choice but by conditions of life, such as being too young (nonage, 1983 CIC 1083) or being too closely related to another person (consanguinity, 1983 CIC 1091). Clearly some marriage impediments last only for a time or apply only in regard to certain potential spouses while others are permanent and universal.
But, getting back to Martin’s claim, the list of impediments by which one is prevented from marrying in the Church is taxatively presented in the Code of Canon Law (1983 CIC 1075) and, search that Code from start to finish, one will not find any of Martin’s subjects (lesbians, gays, bi-sexuals, and/or transgenders) listed as being impeded from marriage. In no wise, whether by incurrence of an impediment by choice or by imposition, does Church law or teaching require such persons to be celibate at all, let alone for their entire lives.
Second—and this is a guess born not simply of Martin’s own words earlier in the clip linked above, but of my seeing people muff these distinctions for many decades—Martin might be confusing “celibacy” (the choice not to marry) with “continence” (the choice to refrain from sexual relations) and, assuming his acceptance of settled Church teaching that sexual relations are only for married couples, Martin might be trying to say that Church teaching on the “continence” to which all non-married persons are called has not been “received” by at least some of the groups Martin has in mind and that they do not feel bound to observe it.
See also “Homosexuality and Authentic Freedom“