Ah, rentals. They were a staple of my NES days. I rented often enough that when I got my collection back from my parents I was shocked at how few I actually owned vs. how many I fondly remembered playing frequently. I found a handwritten inventory I made prior to storing it away and I confirmed they were all there. (I was a weird kid)
What I remember was...
Warning: Old man, unresearched, ramblings
That around the shift from cartridges to discs there was a big push to make rental against licensing rights. Cartridges were a pain to duplicate but CDs? Those were simple, same with DVDs publishers got nervous. This fight was already happening with used PC software sales. I also think the rental joints were getting fatigued with the number of consoles and formats and short shelf life. Compared to a video where a tape or, better yet a disc, could see a decade or more of service. Games were a secondary business for them anyway.
Disc based games also provided a way to reduce the need for game rentals, demo discs. When discs came along, any magazine worth its purchase price had a disc with all the latest games on it. Stores were also getting in on this with stacks of demos near the register to draw in future purchases. At first the demo discs in stores were about $10, then near $5 and finally free. While many were interactive, some were just videos of gameplay. The need for rentals was drying up fast.
Then came digital. Consoles are plugged into the net, games are just 1s and 0s, download the demos and skip having to buy magazines or stop by stores. Same goes for trailers and gameplay footage.
Plus by this time you could do a quick search online and find everything you ever needed to know about a game. These days, with the rise of things like Twitch the demos themselves are seen as unneccisary by many developers and you usually just get trailers and video streamed from other players and reviewers. Things have changed drastically from the days of the occasional magazine, heresay on the playground and even pay-per-minute telephone tip lines.
Back then you were far more likely to pay full price for a crap game. rental was not just fun, it was almost a financial necessity. Now you can watch reviews, watch your friends play live, download it in minutes or have Amazon dispatch a drone and have a physical copy in under an hour. Not much call for rentals anymore.
End of rambling.