There is The Bride if Haebak with Nam Joo-Hyuk as the god of water but I won't recommend it...

I haven’t seen My Roommate is a Gumiho, so these may be farther afield than you want, but here’s my attempt.

I think Hotel del Luna falls in this category nicely. Man-wol is undoubtedly god-like in her abilities and immortality, and there is an actual god (or really seven with the same face) running around meddling with things when she feels like it. Lots of interactions with mere mortals (though most of them have succumbed to their mortality already), plus you get to watch IU swanning around a grand hotel looking fabulous and drinking champagne.

Tomorrow probably also works here. There are lots of grim reapers and other members of the afterlife team, and the different kinds of reapers get to interact with mortals in different ways, either by escorting them to the afterlife or by trying to prevent their deaths. Rowoon also functions as a mortal in lots of ways in this story, because he’s such a noob and he’s only there temporarily.

Bride of Habaek is the most literal “descending to earth” example that I can think of, but I don’t really recommend it, except to stare in awe and admiration at Nam Joo-hyuk’s gorgeous suits. All the patterns and piping you could ever want.

And then this might be a stretch, but maybe Bulgasal: Immortal Souls? There are no gods here, but plenty of monsters with supernatural powers, some ambiguous and some definitely bad. I loved the found family here, but the tone is much darker in this drama, and less hijink-y, so it might not be what you’re looking for.

A Korean Odyssey / Hwayugi. I personally didn’t like this one, but I know other beanies did. I’m not a big fan of Lee Seung-gi but I thought this was one of his better performances. His character and the other side characters were fun but sadly the female lead was written very blandly, which was intentional I think but idk it didn’t really work for me.

Kokdu's a grim reaper, so the most popular recommendation would be Goblin, which has rich world-building, the best bromance, and Gong Yoo.

Other mythological deities include
Hwayugi's Monkey King and Bull Demon King
Arang and the Magistrate's Jade Emperor and King of the Underworld
Doom at Your Service's Doom and goddess

The Legend/ The Story of the Four Gods.

Taleof gumiho is another one. Lots of gumihos and a few gods. I love every part of this show except for the "romance".

It is not a k-drama but the gold standard for angelic guidance: Clarence from IT'S A WONDERFUL LIFE.

Kim Bum as the angel in Padam Padam is the most heavenly (in every sense) mythological figure I can think of. Truly breathtaking visual effects showing him sprouting wings and then flying.

Another heavenly being descending to Earth is Kim Soo-Hyun in You From Another Star. Technically, he's an ET, not a god, but he IS endowed with supernatural powers (including the ability to steal my heart through the tv screen!).

Grim reapers appear in a number of shows, including The Uncanny Counter, Goblin, and Tomorrow.

Can I recommend a Cdrama - Love between Fairy and Devil? Both of them (and some enemies and friends) descend to Earth at one point to fulfill their tribulations or something. They are on Earth for a short time but I think this also fits the bill.

Angel’s Last Mission: Love. Shin Hye-sun was amazing, as always. The rules of heaven left me a little confused, though.

49 Days had grim reaper, right?
Also Fairy Mama whatever drama with Moon Chae Won, but I've heard it's not good at all...
Currently-in-between-its-two-parts Island that we here enjoyed trash-watching has gods, demons, folks with holy and magical powers and who knows what else.
Among upcoming shows there's a romcom about fallen cupid with Jang Dong Yoon and Nana. It's supposed to come out this year, I think.

So, of course, Goblin with Gong Yoo. The dieties here would be Lee El, Lee Dong Wook, Yook Sung Jae and Gong Yoo.

Lee Dong wook plays another diety in Tale of the Nine Tailed and with Kim Bum playing his brother, Lord have mercy! Season 2 is eminent!

The immediate three I can remember that have deities interacting (meddling) with humans are:
Arang and the Magistrate
Mystic Pop-Up Bar
Tale of the Nine Tailed

Well, depending on your definition of deity, these are all shows I'd recommend:

Doom At Your Service (I will forever love this drama, and I think Doom counts as a deity of sorts)
Mystic Pop Up Bar (lots of side character gods, and a bit of a stretch for some of our main characters too)
Angel's Last Mission: Love (he's an angel. That counts, right?
Goblin (also filled with reapers, a god, etc.)
When the Devil Calls Your Name (This drama involves God and the Devil, even though they're not our main leads)
Tale of the Nine Tailed (He's a Gumiho... and a mountain god! Bonus lots of other gods too)

And a few I watched but wouldn't recommend:
Aarange and the Magistrate (I could never get into this drama... I think it may be because Shin Min Ah is not my favorite actress, but also it was just hard for me to get into)
The Bride of Habaek (I... legit don't remember this drama mostly. Thus it was forgettable)

When it comes to Gumiho dramas I think My Girlfriend Is A Gumiho is the superior of My Roommate - but it did come out in like 2012 or something so in some respects it is dated.

Others I liked that were mentioned above are Korean Odyssey and Mystic Pop Up Bar.

Scripting your destiny is a drama few seemed to watched that meets this criteria and I am happy to plug here if it gets it more views.

I was more fond of 'Doom At Your Service' than most posters here were. I think the series fell victim to the expectations game. People were expecting hijinks and 'fun' adventures. If to take the title literally and go in expecting the personification of Doom to be the main character than you'll more likely enjoy the series for what it was rather than what you were expecting it to be,

GOBLIN: THE GREAT AND LONELY GOD is both unique and yet spot on. What is unique is the idea of our ML having to be a god- but only temporarily (a mere nine hundred years) and as a punishment.