On GOG's site:
https://www.gog.com/support/website_help/downloads_and_gamesWhat does it mean that games on GOG.com are DRM-free?
It basically means that you actually own the games bought at GOG.com. Once you download a game, you can install it on any computer and re-download it whenever you want, as many times as you need.
The situation is probably similar with ShinyLoot, as long as you get a game from them that is labelled "DRM-free." They also sell games which are not DRM-free, and those might have limited activations depending on the publisher agreement. From ShinyLoot
http://www.shinyloot.com/faq3. How many times can I download a purchased game?
Every game can be downloaded and installed as many times as you want. We don't allow any games on the site with what we feel is obtrusive DRM such as SecuROM or Tages.
Steam will probably track installations with their client software.
However they don't limit the number of times you can download and install. They just need to know that it's you downloading, and if you download using a computer on the other side of the world from your usual computer, they will get suspicious.
Big Fish allows multiple installs on multiple computers. I've never heard of anyone having a problem redownloading from them as long as their client was working properly.
You should look at the FAQ on the site you're interested for details.