Per the wiki article I linked, they are actually federal police officers, it's just that Canadian Pacific appoints them:
> They are duly appointed and armed federal police officers that gather their authority in Canada via the Railway Safety Act as well as other acts.
Canadian Pacific is nearly 150 years old, I would bet that the Canadian government didn't want to be on the hook for policing such a massive geographic footprint for a private business, but at the same time did want to ensure that an industry that was vital to national security was secured. The alternative was probably nationalizing the entire business, which they likely also didn't have the stomach for.
I'm not an expert but I know there is a long history of railway police having the power of sworn officers. They are effectively quasi-governmental. (Although there is a clear conflict of interest when it comes to choosing to pursue crimes that aren't commercially relevant)
I guess technically? The first Canadian railway was opened in 1836 (while CPR wouldn't be opened until 1885). Canada gained self-governance in 1867 but it was endorsed by the British government and didn't radically change the administrative structure so I feel like your statement is not particularly accurate.
For the rest of the continent: North America is commonly defined as the US, Canada and Mexico - Mexico's first rail system was established in 1837 sixteen years after independence in 1821 and the US's first railroad was built in 1827 just over fifty years after independence.
The CPR was done by 1885. Alberta and Saskatchewan weren't provinces until 1905. The original transcontinental railroad in the US was finished in 1869. Utah didn't become a state until 1896.
These places were very much the frontier when the railroads were built. There was minimal law enforcement provided by the barely-existent territorial governments and the railroads responded by hiring private security (famously Union Pacific hired Pinkerton) and building their own private law enforcement capacity and this was eventually formalized by laws in both countries permitting the practice of railroads having private police.
Much less familiar with the relevant Mexican history.