Canon Law says:
Canon 1248 §1. A person who assists at a Mass celebrated anywhere in a Catholic rite either on the feast day itself or in the evening of the preceding day satisfies the obligation of participating in the Mass.
Code of Canon Law: New English Translation. (1998). (p. 384). Washington, DC: Canon Law Society of America.
So the answer is yes, any Catholic rite will fulfill one's obligation.
A note, however: The Anglican Use liturgy and the Extraordinary Form are not considered distinct Rites as the term is used.
Also, there are 22 Eastern Catholic Churches sui juris, but only a handful of Rites:
- Coptic, and
There are multiple Churches sui juris that use the some of the rites (e.g., the Byzantine rite: Ukrainian, Melkite, Italo-Greek, Ruthenian, etc.) and that's where the 22 comes from.