I think the reason renting hasn't made sense with digital is that it doesn't fill a need. Some tech video about rental explained that originally, video rental made sense because VHS tapes were expensive to make. The tapes, but also the process of duplicating tapes was expensive, since you had to run the tape machines for the time needed to copy them. So you had big banks of tape copying machines, it was labor intensive and it was slow: note that you'd have to start both recorder and player, and after recording a copy, you'd have to rewind the original each time. You're constantly loading and unloading tapes, hitting play, record, stop, rewind. Renting VHS tapes thus spread that cost out over multiple people, since it really did cost $30 to make one and you couldn't realistically lower the price.
DVDs were much cheaper to make: a machine just stamps a never-ending stream of blank discs and you pay people to shove them in cases. Note that video rental stores started dying out well before streaming became the viable go-to option for most people. Streaming was just the nail in the coffin. You can make cheap DVDs of movies and sell for $2 in a case.
In 1998, when DVDs were emerging as the new video medium, Warner Bros. offered CEO John Antioco an exclusive rental deal. Blockbuster was to have rights to rent new DVD releases for a period of time before they went on sale to the general public. The studio was to receive 40% of rental revenues in return, which was the same deal already in place for VHS rentals. Blockbuster turned the offer down, and the studio responded by lowering its DVD wholesale price in order to compete with the rental industry. Walmart seized the opportunity and in a few years surpassed Blockbuster as the studios' single largest source of revenue. Other mass retailers soon followed suit.
So, DVDs actually killed Blockbuster, not streaming. There's very little difference between the price you can afford to sell DVDs and the price at which you can afford to rent them. The concept of rental only makes sense when you need to spread the cost out of some scarce or expensive-to-make thing among multiple people. It makes no sense as a match for digital goods.
EDIT: to the point, imagine you have a rental for a game, and you charge some percentage based on time you played vs full time in the game. You can get plenty of games for say $5 that give you say 50 hours of game time. Are they going to charge you 10 cents an hour? One issue is that the first hour of content may have cost "X" to produce, but the first two hours of content definitely don't cost "2X" to produce: they generally cost a lot less than 2X because the development costs of code and assets are spread across the content and play time. So, there's a big problem here in that for a single-player game, the idea of "pay per hour" doesn't match where the actual development costs were, so it's going to be suboptimal. For example, say you have a new game that theoretically would go for 40 hours, and based on expected sales you can afford to sell it for $40, as a complete game. If you instead charge people $1 per hour, then you're actually going to be losing money, since many players will only play a little, you'll only make that $40 off people who finish the game. Say the average person only sees half the game, you're now
losing money and you'd be forced to raise the hourly price, say to $2 per hour, so people who play the whole game will have paid $80.