The main between a launcher and a store is how many people have transacted on your platform once and have a credit card saved on file. Epic has secured "1st time payment" from a huge swath of players. This is such a huge and rare opportunity, I'd be surprised if they're not making moves towards becoming a Steam competitor, especially given Tim Sweeny's historically bitter conflict with gatekeepers such as the Windows Store.
Battle.net is very popular. There are tens of millions of players that play Hearthstone, Overwatch, WoW, SC2, Diablo 2. All of them launch the games by opening the Battle.net launcher. You can buy and pre order games and game content through the launcher also. Plus it also acts as a social network, you can add friends via their Battle.net tags and chat with them, spectate their games, challenge them to a duel etc. I agree Steam is probably number one but Battle.net and Origin are not small either. They each have millions of not 10s of millions of users I would imagine.
It's pretty common for AAA games to not be available on Steam now. Blizzard never used it, and EA, Activision, Microsoft and Epic have pivoted to releasing exclusively on their own platforms.
Ubisoft still releases on Steam but requires Steam buyers to install and log into Uplay regardless, which feels like preparation for abandoning Steam once enough users have Uplay installed.
Which makes the experience frankly painful in my experience. You have launchers launching launchers etc... I bought some Ubisoft games on steam but now I can't play them because when I launch them they ask for my uplay login and for some reason it doesn't work anymore (I could reset it but I couldn't be bothered).
It also generally doesn't play well with Steam "family sharing" that lets you share your games with family members without having to share the same steam session.
I don't like DRM very much but I do use Steam and Spotify because they mostly just work and don't usually get in the way. Cloud saves are pretty convenient too. I haven't bought a Ubisoft or EA game in a long time, mostly because I know it's going to be a pain to deal with their launchers.
If only I could buy a boxed game and not have to deal with any of that nonsense like back in the days... Some days I long for CD keys.
Yes? I don't see how anyone could claim otherwise.
Battle.net is a store, because it sells games you can purchase, including expansion pack sales, microtransaction sales, etc.