It's very unlikey they go out of business as a result of this (or other recent fuckups). They are still currently too big in the gaming space and have made too much money from previous successful ventures for this to be a tremendous issue.
Activision (the parent company) is finding some success again with the Call of Duty Franchise and owns some successful mobile gaming companies as well.
Blizzard itself, however, has
major profitability problems and employee problems.
Firstly - a lot of the "Blizzard" key staff have left the company - mainly the pioneers of Starcraft, Warcraft, and Diablo, the kind of people who are capable of making new, engaging games. They have not successful replaced them.
Secondly - Blizzard (even Pre-Merger) has been struggling to release quality products. It was, including post merger, 12 years between the release of Diablo 2 and Diablo 3 (and many people feel Diablo 3 is vastly inferior). It was also 12 years between the release of Starcraft and Starcraft 2

art 1 (with many people feeling that Starcraft 2 was vastly inferior). The main problem with this is that SC2/Diablo 3 cost a lot of money to develop and if people don't pick those games up, that money is wasted. They've recently gone into new IPs but the games themselves are not remarkably innovative.
Overwatch borrows a lot from Team Fortress/MOBA games.
Heroes of the Storm is a very-late-to-the-party DOTA/LOL clone.
Hearthstone is a card game - It's a card game, although not a horrific one.
Thirdly - Blizzard is skitzophrenic about how to make money. This isn't solely on them (as the market is changing as well) but they have no idea how to effectively monetize these games - even when they are successful. The real killer here is how hard Blizzard is trying to get into e-sports, they're funneling
tons of cash into Hearthstone (which has a small following), Overwatch (which has an OK following, but not enough for a fucking literal league), Heroes of the Storm (which had no scene ever, and Blizzard mercy killed not too long ago), Starcraft 2 (which has a small scene), and WoW (which has a very small scene).
World of Warcraft, in 2004 (to ~2010, depending on who you ask) was 100% king shit of MMORPGs for all time. However, in 2020 the game is stagnating horribly under the weight of several mediocre expansions and no longer is the juggernaut it once was. Final Fantasy 14 likely has more subscribers and is more highly regarded, despite starting so bad that SquareEnix was too embarassed to sell it for a while.
They (very recently) half-assed a Warcraft 3 remaster - which should have been a literal license to print money is now instead an incredibly thick black eye; on top of all of the ones they've recently gotten.
Not only does Blizzard waste money, but they aren't clear on how to make it. They've tried
everything over the last few years - episodic releases, costume packs, lootboxes, card packs, character packs, expansions passes, cash shops, subscriptions, selling literal in-game currency, and sometimes
multiple efforts per game.
For example - In World of Warcraft - there is the base game, the most recent expansion, a subscription fee, a cash shop,
and you can buy gold with real dollars. Diablo 3 has the base game, the expansion, and a seperate character pass for the Necromancer ($15). Starcraft 2 was released episodically (3 parts) and still has multiple, additional DLCs as well ($4.99 for co-op commanders, $15 for extra SP story stuff).
It's a lot of DLC for bad-to-medicorely recieved games in a market that's pushing back against gigantic piles of DLC.
Blizzard cost Activision nearly $19
billion dollars in 2008 and another $6
billion dollars in 2013 and it's very unlikely that Activison has made $25+ billion off of Blizzard. Blizzard as we know it now is in dire need of a restructuring and Activision is likely to do it in order to see some actual returns on their investment.