Tahm Kench has some strong versatility that is capitalized by this build. He is still very tanky, he can wave clear any lane, he still excels in team fights, and in a one vs. one setting there are very few champions that can outright kill him.
Something to note is that this is more of a late game build, you need about three full items to do it justice, but tahm kench as a champion can have a strong early game, because he can really punish bad enemy decisions.

If you only read one section of this build, the most important one is the "Main mechanics of the play style"

With this build we want to, obviously, split push. We also want to become a distraction, with our zz portal we can push down lanes and towers very quickly. Titanic and the passive of our ult allows us to wave clear, as well as, doing tons of damage in any fight we are in. we can run back and forth between different lanes with the speed from our items and masteries, our teleport, and our ult. Overall we can split push, draw multiple people to the lane to try and kills us, then be on the other side of the map for the team fight.

Tahm kench is not a difficult champion, but so many people don't understand a key part of his play style. If you have three stacks of his passive, the q will stun the enemy if you hit them.
From this information we get our main fighting order. Get three stacks of the passive, using basic attacks. Then use q, which will apply the stun if you hit them. with the attack speed in the masteries we can auto attack one too two times, which will proc our undying grasp. Then use w too swallow them, by the time they are ejected grasp and your q will be close to being off cd again.
This does a fair amount of dmg, but it also restore your own health and reduces the time the enemy will be actively attacking you. If you can do this, one champion should almost never be able to kill you on their own, so wherever you go, you draw two of the enemy team.
Something to note is that the auto attack reset from titanic does not seem to proc your passive.

A big factor of tahm kench is his adaptability to any situation. Going with this theme, except for zz portal, and titan, all the other items can be switched out for something that matches the situation better.
The runes can be swapped for most anything, so long as they work with Tahm's strengths and your play style.
Masteries can easily be swapped around, just keep some of the core mastery points,
examples: Grasp, and fury.
For the summoner spells, teleport is a must have. Ignite is more situational, I use it to have kill pressure in the lane. As well as a counter for high sustain champions in team fights.

The weirdest part of this build is the ability order. Taking grey skin at level one is and odd idea, but it gives you lots of early sustain. As most of the enemy laners will be trying to either poke you down or trade with you. Getting all of your abilities is essential to Tahm as a champion.
From there, the only thing is getting your ult whenever you can. The ability order is up to you and the situation as too what you need. More damage? get Q. want to kill a tank? get W (it does percent health damage). Getting poked down? E is your main ability.

This is a universal build, you can do just about everything. Just keep your eyes on the minimap, and don't be afraid to run from a fight. Remember you can drag one more person with you if you need to retreat.
Gl HF