I went into this map wondering what on earth the CDT was thinking when they released it; having finally cleared it I can safely say it's very reasonably doable, even solo NMHC, provided you know full well what you're doing on the boss fight. My stats are mostly around 4k with no event items used. Summoner has 4k Tower HP/dmg, Adept has 4k Tower Dmg/Rate, Aura Monk has 5k dmg, 3k radius, 2k side stats. My successful runs were fairly comfortable with these stats, you could probably make this work with 3k stats, but I haven't tried it. No idea how well this would hold up in a 4 man group.

Minions will all fit comfortably on a 5DU buff beam. For the DSTs, just jump over the bit of crystal wall you see to get inside the crevasse. It's extremely easy to get into, even without a moon pet, and there's enough buildable space for the buff beam and four stacked DSTs. If you're having trouble getting back onto the rest of the map, just type "killme" in chat for an easy escape. The DSTs take a lot of pressure off the NW and SE cores, which tend to get hit the hardest. Ogres cannot path to the DSTs, and copters/djinn should be dead long before they could even touch them.  Make sure you orient them properly or copters/djinns will eventually destroy them. The auras in the middle are only for the boss fight and can be built just before or during the final wave, and will be sold/resummoned as needed for each phase. Build everything but the center auras during the first wave, as you have plenty of time. You'll have enough mana for everything, and to upgrade two buff beams three times.

Genie King Boss Fight:

The boss is fully immune to generic (non-elemental) damage. He has 320m HP solo, and also takes 75% reduced damage from all sources of player damage I ran with, including pets. This means your 20m NM DPS with hero boost seahorse is only going to do 5m DPS to the boss at best. This limits your hero options to either Jester with a Bloodshot/Emerald Staff, Monk with an elemental pet, or Barbarian with two Emerald Swords from Emerald City.

I used a monk with SL skin, Crystalline Dragon pet from CR3 survival, and Emerald Halberd, 4k hero dmg, 2k hero boost and 2k hero HP, and IMO this is the easiest setup you can bring to the boss fight. The pet can be farmed on insane survival relatively easily. I was lucky enough to get an ult pet this way with 41k base dmg fully upped, but 30k base dmg should be enough for the boss. The main reason I highly recommend a Crystalline Dragon over a seahose is that the horse will often stop attacking the boss to hit the random enemies that will be all around you throughout the fight, resulting in much less DPS to the boss overall. The dragon hits in a large AoE and in my experience did far more DPS to the boss in the actual fight, despite lower DPS numbers on the tavern dummy compared to a seahorse. 

When actually fighting the boss, just circle strafe jump around him while your pet goes to work. Watch out for his eye lasers, they hit very hard! You can also tower boost while fighting him to make your str drain and heal auras more effective. You can melee him as well if you bring an Emerald Halberd, a good one can easily get up to 150k+ base dmg, but it will still pale in comparison to your pet as you'd expect. Once you do roughly 25% of his max hp, or a long amount of time passes, he will move into one of the many lamps spread out on the map. You'll see a large purple line pointing in the direction of which lamp he's moving into. https://imgur.com/HUuS8ao for a map of all the Genie lamp locations, which also tells you where the boss will spawn once he leaves the lamp. (Thank you so much Plane for this map)

The moment the Genie King moves to his lamp, do NOT immediately chase after him! While the genie king is out of his lamp, small djinn will periodically be spawning around the map. Towers will not target them (but I'm fairly sure your auras will damage them) and they can gold any enemy, even ogres, and if left unchecked gold ogres will absolutely destroy your defenses before you can kill the boss, no matter how good your stats. Check all over the map (they have a unique white color on the minimap) and make sure you kill every last one before you start the next phase of the boss. The dragon has exceptionally long reach, and is surprisingly good at killing them.

Only when all the white djinn are dead should you move on to whichever lamp the genie moved to and continue your fight. Before you rub the lamp to let the genie back out, make sure you summon both a str drain and heal aura at the spot where the genie will be summoned. This is where the map linked earlier is so useful, you can place the auras right where the boss will be, and he will not stray from that spot until he goes back into another lamp. Str drain DOES affect the boss, will be improved if you tower boost, and will massively improve your survivability, even if your DPS monk only has 1k tower stats like mine. Once the boss retreats, sell the auras, hunt the white djinn, continue the pattern until the genine king finally falls.

Take the boss fight slowly, make sure you hunt down every last white djinn when you can, and also check on your defenses every so often. The minions hold up pretty well on their own, mages may occasionally need some healing, but I've only ever lost a mage to golden ogres left unchecked. DSTs should take no damage. If a 4k scrub like me can beat this map, then hopefully this guide helps others to do the same. Have fun and good luck!

PS: Don't bother replacing the DSTs with LTs hoping to cheese the boss. The LTs will chain to the boss, but they will not damage him. LTs would likely get destroyed during the boss fight anyways due to stray djinn/copters.