So basically your ult will be on a 35 second CD with no wind dragons and full build, so you'll be able to provide full map vision in late game very often, which is extremely valuable. With 4 wind dragons you'll have a 30 sec CD on R. Also, you'll have a 1.9 second CD on W, which allows for a lot of stuns. What's more hilarious is that you could, in theory, permastun someone since your W gold card stuns for 2 seconds, which is longer than your W CD. This only works against people who haven't built tenacity though, and it only works in 1v1s. But with your short R CDs, finding 1v1s is easy.
When you think about it, this build actually isn't that troll, since you only build the weird items late game. More explanation in the "Playstyle" section

Alternatively, you could pick something like RFC over Chemtech putrifier to sacrifice a little bit of ability haste for some long-range stuns. Chemtech putrifier is pretty much the only item you can replace though, since Liandry's is a good mythic that gives dmg and ability haste, vigilant wardstone gives *1.12 ability haste, and black cleaver and navori quickblades both give more ability haste than any other item in the game (not counting ornn upgraded items).

Since your first few items are AP and cause you to deal decent damage all the way until mid game, just play TF like you would normally play. Your first items are pretty cheap, so you should be able to get them with a little bit of CS. Start spellthief's edge for more gold, and also TF passive allows you to get gold (you get about 3 minions' worth of extra gold in one minion wave, assuming you last hit). After laning phase/mid game, you should start farming like normal mid TF in a sidelane or the jungle. The later items are kind of troll, so you should play safe and provide vision. It's a good thing you're going Liandry's, since it does damage no matter what other items you build. That passive is kinda juicy. Once you get into the late game, you'll be getting a lot of vision with your ult. Even if you're like an item or two off, you'll be able to 1v1 any squishy with your W, since at that point your W cooldown will be about 3 seconds, which still allows you to get lots of stuns.