First error downloading and you'll be having issues with ESO
but with 8GB free Win10 is just as likely to eat all of that with one of the 6 monthly updates & it's generally downloading and leaving all the incremental stuff
Time to get another SSD imo
“Be as a tower, that, firmly set,
Shakes not its top for any blast that blows!” Dante Alighieri, The Divine Comedy
Yeah, I wouldn't recommend a 120GB drive for this game. Generally speaking, you want something with at least double the space you expect to use.
This game takes up 75-80GB, and then theres the PTS installation if you opt for that which takes up twice as much space. On my system, it's about 135GB of data total.
I'd recommend just going for the 250GB drive upgrade and future-proof at least a bit.
(as other posters have mentioned, it's better if you segregate your OS drive from your game installations - you won't have OS processes and game processes competing for buffer space)