We DO have a D&D video game. Sword Coast Legends that came out in late 2015.
To have a new video game now, a new company has to get the rights to the game, which is tricky since Digital Extremes might still have them. Failing that they need to negotiate with WotC, which takes time.
Then they need to make the video game, which also takes *gasp* time. Years.
Well there has been another successful Pathfinder KS that has funded, 500k+ and counting for Pathfinder: Kingmaker a SP game based off the AP where you go forth and settle the Stolen Lands. Looks like its Baldurs Gate/ Pillars of Eternity type isometric graphics.
I didn't back it. Because of the LAST Pathfinder KS video game. Which was Pathfinder Online and god awful.
Will this one be better or be akin to SCL? We don't know and will find out in a year!
I started a thread a long time ago about how to get a successful D&D game off the ground. Since WoTC won't drop 40-200 million+ on a AA+ title I would like a Pillars of Eternity type game to be down and would be willing to settle for a modern 2D 16 bit game a'la Phantasy Star III/IV, Shining Force or a modern "16 bit" Stardew Valley type graphics as long as the story/game was fun.
Pillars of Eternity required $1,100,00 to get off the ground in a bare bones fashion. But that was a company that made video games, had made several successful video games, had the staff and infrastructure, and likely had put some work into the game already.
WotC is a collectable card publishing company that dabbles in books, not a video game company. I'd trust them as much to make a video game as I'd trust them to make dog food or kites. Why would I expect them to make a video game?
The problem is that video games are super expensive and D&D and RPGs are niche.
Look at the Pathfinder game you mention:
https://www.kickstarter.com/projects/owlcatgames/pathfinder-kingmaker
They asked for half a million dollars. And they already have a lot of the game architecture done (it's in Alpha) and done by people with a history in gaming. So it's a safe bet. But they only managed to just fund a few days ago, and there's less than 2 weeks left. It's trending towards $851,711 according to Kicktraq:
http://www.kicktraq.com/projects/owlcatgames/pathfinder-kingmaker/
That puts it below Pathfinder Online, that cleared a million:
http://www.kicktraq.com/projects/1675907842/pathfinder-online-a-fantasy-sandbox-mmo/
(That had a dubious surge in funds at the end that suggest someone internally decided to pay the difference.)
Neither are CLOSE to what Pillars of Eternity made.
Funny thing, Obsidian Entertainment was making a Pathfinder game. They got the licence to Pathfinder in 2014. Why don't we have a Pathfinder game by Obsidian. Because the Pillar's Kickstarter did well and then the game reviewed well and sold really, really well. So Obsidian decided they were better off with Pillars 2.
So why don't we have a D&D game? Because it's cheaper and potentially more profitable for game companies to make their own games. Because a successful game doesn't require a licensed name to succeed, AND video game fans have learned to be super wary of licensed properties, which are typically of dubious quality. Because D&D is too small to attract a number of people to qualify as a successful game.