The dictionary definition has no legal status; that is determined by the Marriage Act regulations of the State or Province. I looked up the Act for Alberta to see what the requirments are here.
Alberta requires a "bride" and a "groom." I think this pretty well demands people of the opposite sex. There must be no lawful causes to prevent the marriage.
Furthermore, The two applicants must swear that "I am not marrying my grandmother, daughter, sister, son or brother who is related by whole blood, half blood or adoption"(!). Medical certificates are required that the applicants are of sound mind and neither is drunk or drugged.

Much fine print about the relationship, etc., most of which refers to "husband" or "wife." Here again, different sexes are implicit.

Ontario Act Regulations clearly state that a marriage between homosexuals is void. The Act goes on to state that "marriages have to be consummated by sexual intercourse between the couple and are voided if impotency..."

Clearly, each province has its own Act with requirements that must be changed to make same-sex marriage legal.

Looked at Texas for comparison. Their Act clearly states "Same sex marriage: No"