Game data would be downloaded ahead of time; the Satellaview came with a game cartridge[0] that gave you a system menu in the form of a JRPG town that looked a bit like EarthBound's Onett. It also had a second slot on the BS-X cartridge that accepted a memory card for storing game downloads onto.

For SoundLink games, the voiceovers would be streamed from a satellite radio channel while the game ran, and they could also issue game commands. Obviously this also meant you could only play a SoundLink game while it was being broadcast. There were periodic reruns in case you missed a game. The closest modern example I could think of would actually be something like 1 vs 100 on the Xbox 360, which only lasted for like a year if I remember.

Other downloadable Satellaview games worked almost exactly like a modern digital download system. You'd have to download the game while it was being broadcast, but could play it later. Except some of them would also have a start-up limit (like 3DS demos) after which the game would expire and refuse to start. Those are easier to preserve than the SoundLink games, assuming you can find an old Satellaview memory pack with the game data still on it.

Some of the 'games' were actually just magazines or text. There's some really odd ones we've discovered over the years. After Nintendo stopped supporting Satellaview[1], St.GIGA tried to repurpose the Satellaview as a program guide for their own satellite radio service using this feature.

Interestingly, there's a handful of SNES games with the same Satellaview memory slot on them that BS-X does - for example, RPG Maker 2[2]. I'm imagining that they distributed RPG Maker games using Satellaview, but Wikipedia also says RPG Maker 2 was available as both a cartridge and a Satellaview download, which seems like it defeats the purpose of having the cartridge also accept Satellaview memory cards.

BTW, if you think this is crazy, wait until you learn about the SEGA Channel, a cable modem that plugged into your Genesis[3].

[0] BS-X: The Story Of The Town Whose Name Was Stolen

[1] Because, among other things, they wanted to build the N64 DD around RANDNet

[2] Not to be confused with RPG Maker 2 on the PlayStation 2, which is actually RPG Maker 5, because international numbering.

[3] Or Mega Drive. I didn't even know Europe had this until I checked Wikipedia!