Does the law require sport clubs to run vulnerable sector checks?

Not at the federal level. The RCMP states that no federal law requires any organization to run vulnerable sector checks, and suggests contacting your provincial or territorial government for more information. A police service may only run one if the position qualifies under the Criminal Records Act; the RCMP says it is an offence to run one if the position does not meet those requirements.

Sources: https://rcmp.ca/en/criminal-records/criminal-record-checks/vulnerable-sector-checks and https://rcmp.ca/en/criminal-records/criminal-record-checks/types-certified-criminal-record-checks