Because he's one of the few devs with true name recognition. All video game awards shows have always been chasing the Oscars but the film industry is full of massive celebrities. Not just stars but directors and even some writers and producers.
So Kojima has that. Plus his work always shows well. It's usually something unique and cinematic.
Which seems a fruitless ambition, the talents required to be great at both are very different, charisma and attractiveness are much more important in the film industry. People will naturally like those stars more because their job is in part to be likable
Even MGS5, which was pretty clearly pushed out before he wanted it to be and broke him up with Konami, was extremely technically sound, just not filled out as much as it should have been.
Because in an industry dominated by yearly rehashed minimum viable products like CoD or AC or Battlefield or the plethora of lootbox infested live services meant to fuck your wallet for easy quick RoI for shareholders, Kojima spends time and resources creating new, novel ideas and taking the artistic medium (yes, games are art despite what capital G Gamers want to say) to new and exciting and interesting places.
This is why Hideo Kojima, Yoko Taro, Fumito Ueda, Hideaki Itsuno, Keiichiro Toyama, Eric Barone, Terry Cavanagh, David Szymanski (etc etc etc, I could go on) all get name recognition.
People always SAY they want games to expand and try new things/don't want the same game every year, but then when someone actually tries, the games get panned as "gimmicky" or "niche" or "pretentious" "pixel graphics indie garbage" or some other flavor of the month phrase gamers use to instantly discredit something that doesn't immediately and specifically cater to every single one of their preconceived demands on what a "game" is and/or should be.
Why other game devs don’t get that much recognition or screen time?
Probably because Geoff Keighle and Hideo Kojima are great friends. Game Awards announced 30 seconds limit for speeches, but those only apply to everyone else, not friends.
The same reason people thought star wars the last Jedi was good, if you just make a fucked up enough narrative and pretend it's high brow instead of contrived, you can fool the elitists into believing they're smart for liking it.