Demos used to be everywhere back in the day! I think they have a huge impact, because it's a way to try to play a game without dumping all the money on it without knowing what the gameplay is like and if its actually fun.

When I was a kid, DOOM having the first episode of the game available as shareware was huge and I used to walk to my friends place after school and watch him play until he would get bored and let me play for a while.

From an old interview in 1999 with John Carmack about this very subject (emphasis mine):

Carmack: DOOM 2 was explicitly a commercial release. We sort of half heartedly did some shareware distribution with Quake, but I think the industry has almost unanimously decided that the three or so level demo is the best test vehicle.

A lot of people consider themselves to have "finished DOOM" when they just finished the shareware episode.

Funny how Steam has been making sales and events around demos for a while (called Next Fests) and some games absolutely blow up out of nowhere thanks to them.

Also some people think FF16 having a demo was some weird, oddball marketing move by Square Enix, except they have been making "try now, continue later" demos for games since Bravely Default.