When video rental was supplanted by video streaming in the late 2000s, game rental mostly went down with it. However, unlike video, game rental was replaced with digital stores, allowing you to own digital copies of games and download them at any time to play them. It wasn't until recent services like Xbox Game Pass that subscription models similar to video streaming started to gain popularity.
Cloud gaming is an alternative to digital download, where the game is instead run on a server, receiving control inputs and streaming the resulting video back to the player over the internet.
There are two key advantages to this idea: the convenience of being able to play games without download, and the ability to play the latest big games without buying an expensive computer or console to be able to run them.
There are two sides to the problems with cloud gaming. The first is technical, as cloud gaming requires transmitting a large amount of data with very low latency to be a good experience. The second is more socio-economic, to do with pricing schemes, the games available on the service, and how the customer gains access to them.
Google Stadia is a very good case study for cloud gaming. On the one hand, the technology behind it is very sound. The engineers at Google identified one of the key concerns with cloud gaming - added latency - and created a smart solution for it. Because it's Google, they can leverage existing datacenters around the world to create very short travel time for packets, just a few ms, so the problem isn't the transmission of data, but the encoding and decoding. This is another area Google already excels in, as there have been years of development for codecs for YouTube to allow responsive video playback and live-streaming with a delay of only a few seconds. However, latency for a video game should at least be under 100ms to be an acceptable experience, and ideally under 50ms for a good experience - and that's including 10-70ms of latency introduced by the display itself. Another area they use for optimisation is in the transmission protocols, where they've implemented their own version of Bottleneck Bandwith and Round-trip propagation time. Another key optimisation is with buffering. With the incredibly low latency required for cloud gaming, the window within which a packet is still useful is incredibly short, making buffering not only unhelpful, but actively detrimental as it can delay the arrival of actually useful packets. So, to disable buffering, Google uses WebRTC extensions on the receiver-side.
However, despite their impressive technology, Google Stadia is widely considered a failure. The reasons behind this are fairly simple - Google tried to create Stadia as a service with its own digital storefront, entering a highly competitive and unfamiliar market. They spent tens of millions of dollars acquiring titles to put on their service, but even then the selection of games available were considered unsatisfactory. On top of this, their pricing model has customers subscribe to the service, but then also purchase the games they want to play on Stadia's storefront, which goes against usual customer expectations of a subscription model (though a small selection of games were included with the subscription)