Criminal Code 293 outlaws polygamy and bigamy, and identifies as an offender
Every one who
(a) practises or enters into or in any manner agrees or consents to
practise or enter into
(i) any form of polygamy, or
(ii) any kind of conjugal union with more than one person at the same
whether or not it is by law recognized as a binding form of marriage,
(b) celebrates, assists or is a party to a rite, ceremony, contract or
consent that purports to sanction a relationship mentioned in
subparagraph (a)(i) or (ii)
In other words, it is against the law to go through the ceremony with multiple partners, and to "enter into a conjugal union", even if not solemnized in any particular fashion. "Common law marriage" is broadly recognized in Canada (except in Quebec), with specific details governed by the province. This too is a case where people who "act as if" married are treated as actually married, given certain circumstances (which exist in a polygamous marriage).
The question of having children is not relevant to the law, indeed having sex is not a requirement for something to be deemed a polygamous marriage, and the law against polygamy also says
nor is it necessary on the trial to prove that the persons who are
alleged to have entered into the relationship had or intended to have
In this particular case, we do not know the specific details, but it is reasonable to assume that there was no posturing or faking, and there were multiple solemnization ceremonies, so the polygamy is overt. The claim is that it is constitutionally protected.