This dude conveniently appears at the end of chapter 3 to throw one final kink into Ruth and Boaz's happily-ever-after.
While they're sharing a romantic moment on the threshing floor Boaz mentions that he'd like to marry Ruth, but that "there is another kinsman more closely related than [he]" (3:12). Is Boaz just afraid of commitment? Or does this guy pose a real threat to our heroine's happy ending?
Turns out, Boaz is just covering his bases. But he has to play it cool to get what he wants. Boaz finds the other kinsman and then stages an elaborate negotiation. First, he offers the man some choice land—"I will redeem it" (4:4)—then he throws in the tiny little fact that if he redeems this land he will be forced to marry Ruth and have children in her dead husband's name. The other kinsman quickly does an about face—"I cannot redeem it for myself without damaging my own inheritance. Take my right of redemption yourself, for I cannot redeem it" (4:6). Well played, Boaz.
The two men then go on to strike an elaborate bargain (complete with sandal exchanges) and the deal is done. Ruth and Boaz get what they want, and the other kinsman is none the wiser.
So why include this guy at all? Well, the author may just be upping the stakes one last time. After all Ruth has been through, she still may not be able to marry Boaz? Not cool. In the end, though, it's clear that the other kinsman doesn't really pose much of a threat. In a book where names matter, this guy doesn't even get one. That's how little a role he actually plays in the lives of Ruth and Boaz.
Better luck next time, other random guy.