The videogame publisher gets one extra unit sold, and the rental store taps into a lucrative slice of that game's potential market.
You can say that it creates "more informed" gamers, or that the people who rent (and don't buy the games later) aren't likely to buy games in the first place. I know I myself grew up renting games, and now I buy more of them than I can play and/or afford. But those exact same arguments apply to piracy.
IIRC, back in the NES era, when videogame rentals became all the rage, Nintendo spearheaded an attempt to make renting games illegal, to protect their third parties. They joined up with Microsoft, and a couple other related groups, who were concerned about rentals of computer software.
They got some lobbyists, and went to Washington, to go buy some congressmen. But Blockbuster and the other rental chains were already in Washington, and had longer-standing, higher-paying relationships.
The publishers couldn't win, and then Blockbuster made Microsoft an offer. So Microsoft cut Nintendo loose to twist in the wind, Blockbuster stepped out of the way for Microsoft, and a law was passed saying it's illegal to rent out computer software, but console games were fair game.
AFAIK, it is the position of Nintendo, Sony (actually, I honestly suspect it's just lyp service from them, and they even quietly support piracy, as it's in their interests), and ironically, Microsoft too now, that game rentals are harmful, but Blockbuster is just too big and important in the industry to even dare risk pissing off.