People do this for SEO purposes. They think that this increases the amount of backlinks to their site, thus increasing their rank in Google and other search engines.
This is less true than it used to be, but people still do it.
Just feels like such an odd play lol. If they could organically generate leads/traffic that I'd be willing to get extorted over, then surely they would also have the means to start a marketing agency that I'd be willing to pay far more for?
The fraudulent domains are only sending traffic to OP.
My guess is that they want to either phish visitors, or they want to ask OP for affiliate revenue, like a digital version of the guys who wash your windshield or your shoes without asking first, and then ask for money.
Or planning to threaten to divert organic traffic through the impersonation domains away from the canonical domain, if you don't pay them.
This is less true than it used to be, but people still do it.