For some games yes but some download through a different client and some are stand alone that you just 'download' and play and are not linked to steam/origin/uplay etc.
For origin/uplay/steam games generally you get a code which you put into the relevant client and it downloads the game for you. But sometimes you download the game first (like I recently have with AC3 from greenman gaming) and install it to the relevant client after.
All digital stores have a description under the title like: You have to register your account on steam,origin etc .If there is no description that means you have to download straight from store where did you got your game
Yea like others have said they're very easy to use. Normally the deal is, you buy the game, you get an email 2 minutes later with a unique code which will normally explain how to retrieve your download and then for Steam you log in, click 'add game' in the bottom left I think and there will be an option to activate a code. Just paste the unique code in and it's all sorted. I was a bit hesitant the first time I used it but it really is very easy.
One thing I don't like though is using a website's own client. I don't mind Origin and Steam but I'm a bit wary about others.