It's still listed as 'owned', but for some reason it disappears from your actual library when uninstalled, so you have to install it from the store. :|
Save money? Brother I know people who have spent thousands on Dota 2.
Dota 2 is very different from most other F2P games though, in that a huge amount of people buy a reasonable amount of microtransactions, instead of the game relying solely on whales.
I may or may not be a whale since I've probably spent somewhere in the range of $300 on the game throughout the years.
Anyway, 700 hours isn't necessarily that much either. At that point you're simply above average at the game, and not necessarily any good. I've 1642 hours clocked (atleast 200 of those spent watching tournaments, mind you) and I'm somewhere above 4000 MMR, which puts me in the top 5% (last time I checked the stats, I haven't in a while, mind.) yet... I'm not exactly great at the game. I'm probably outright "good", but not great or anything.
Dota is a weird beast.
Edit: Yeah, two of the guys I usually play with have over 2800 hours played, one is about a dozen away from 4900 hours and another Steam friend of mine is at a sky-high 12585 hours. Although to be fair, he lives off of making dota cosmetics, so I'd imagine half those hours are ones spent on that.