Looking at the quotes from the regulations summary (see below). The rope lure would seem to fit the definition of angling rather than 'non-angling methods'. According to the regulations, angling require a line; it doesn't mention hook.
Non-angling methods of capturing fish include: dip nets, seine nets, spears, and bow & arrow. The rope lure certainly doesn't fit any of those.
Based on what I see on the summary of regulations, I would interpret the rope lure as 'angling' rather than a 'non-angling method of capturing fish'
As per the regulations summary:
Angling – Angling means fishing with a line that is held in the hand or attached to a rod that is held in the hand or closely attended.
Residents and non-Canadian residents with a valid recreational fishing licence may fish with one dip net, one seine net, one spear or a bow and arrow for the species and during the periods outlined below.
Dip nets may be no more than 183 cm (6 ft.) on each side if square, or 183 cm (6 ft.) in diameter, if circular.
Seine nets may be no more than 10 m (32.8 ft.) long and 2 m (6.5 ft.) high.
Spears cannot be possessed on or within 30 m (98 ft.) of the edge of any waterbody except when fishing for carp and white sucker as described on this page. Northern Pike spearing is not allowed.
Bow and arrow: includes all longbows. Longbows are considered a firearm under the Fish and Wildlife Conservation Act.