Yes I do think that gay marriage should be in the Constitution, whether called "marriage" or something else.
I think this because it is widely accepted that a same-sex relationship is as valid as a heterosexual one. Allowing this to be recognised in law is legal confirmation of this stance. It means that people in same-sex relationships can have them affirmed publicly instead of feeling like second-class citizens. It also, in my opinion, encourages a same-sex couple to take the relationship more seriously as it is a legal entity.