Yes, “any other law of Canada” means any other federal law. It does not literally mean any other law of Canada. This was decided by the Supreme Court in Roberts, in 1989. That case involved interpreting section 101 of the Constitution. It includes federal statutes or federal common law.
Typically, federal legislation says any law of Canada or of a province or “any other law” if it's used to denote wider application. The reading of “any other law of Canada” makes more sense in this if you look at paragraphs 3(a) and 3(b) of the definition as well. Paragraph 3(a) would become redundant, because it already says it has to be beyond the authority and capacity of a province. Paragraph 3(b) doesn't have anything to do with provincial jurisdiction.
Realistically, once the executive has decided that the criteria under the chapeau of paragraphs 3(a) and 3(b) are met, all they need to look to, then, is whether or not there are other federal statutes for them before they invoke the Emergencies Act.