No, “cultural genocide” is not genocide. There is a pretty clear legal definition:

… any of the following acts committed with intent to destroy, in whole or in part, a national, ethnical, racial or religious group, as such:

(a) Killing members of the group; (b) Causing serious bodily or mental harm to members of the group; © Deliberately inflicting on the group conditions of life calculated to bring about its physical destruction in whole or in part; (d) Imposing measures intended to prevent births within the group; (e) Forcibly transferring children of the group to another group.

Fair enough, but the term genocide is far too inclusive, I’ve heard people use cultural genocide instead.