https://www.gamespot.com/articles/ps4s-playstation-now-adds-downloadable-games-makin/1100-6461936/

The PlayStation Now service has gotten a big upgrade today, with the announcement that subscribers can now download games in addition to the existing streaming option. The company boasts that "almost all" of the PS4 games on the service can be downloaded, along with the lineup of PS2 games. This doesn't include the line-up of PS3 games.

Your downloaded games will support any DLC or add-ons, and you don't need a PlayStation Plus membership to play online multiplayer for games through PS Now. You will need a PS Plus subscription to transfer any cloud saves from the streaming version to the downloaded version, however. Also, your PS4 will need to check in with the internet every few days to verify your PS Now subscription. Sony says the download option will be rolling out over the next few days, so if you don't see it yet, it should show up soon. Check out the library to see what's on tap.