You know back in the day, I considered myself the kogiest of Kogs. Learned to play him in every role. Jungled with him even in season 3. Learned to like him mid. Lost my mind when they thought he needed the mana cost on his W buffed to 0.
That being said, I don't main him anymore because I like Tahm more. I like his playstyle, lore, (and voraphillia was a factor. I regret nothing.) But I still keep Kog in my back pocket (which now that I think about it I, I played him for vore related reasons also) and have a couple things to say about the rework.
Old Kog's kit was flawless. It was the epitome of balance, visceral power, flexibility, and impact. You could build him so many ways it was silly. Not only that, but he always felt like an artillery cannon. Behind or ahead, he had an advantage at a distance.
New Kog has 2 differences. The first is the demand for on-hit Kog. You can try to math it up and figure out how much the damage difference is, but you will always end up with more damage in the end game stats with on-hit Kog for one reason or another.
Secondly, his ult is now an execute. I actually like this change, because that's what I use it for. I didn't like using it for poke. It felt wrong. Other people will tell you that I'm an idiot for not using it as a poke, but after some 1000 games with him, I feel like the ult has improved.
That's not what this post is about though. Why should you play Kog as an adc? My answer: you shouldn't. Kog is not an ADC and never has been or will be. In season 3, ADC Kog Maw's highest winrate item was Infinity Edge. Does that make sense? Infinity Edge would certainly make less sense now with his attack speed doubling making crit so oddly wasteful. ADC Kog scales best with on-hit, lifesteal, and attack speed. Big emphasis on attack speed. With the recent changes to his W, there is only 2 items that really strike a chord with his kit: Blade of the Ruined King and Guinsoo's. That being said, Kog is having less and less business fiddling around in the mega death botlane when he is super squishy, requires specific team comps to be played effectively (have fun setting that up), and the new ADC itemization puts a middle finger right in his eye socket. But if you do, remember that his advantages are wicked damage and awesome range. End of story. He can eat tanks, but that is something I found you can only learn how to do after, say, 60 games with him. It's a bit like learning how to blow a bubble when you're 7. It's hard for me to just tell you why that is, but I can say that he is still the best at it. Vayne is actually somewhat bad at proper tank busting.
So I'm going to tell you two secrets I really shouldn't be giving away. I hope that most people who read this will think I'm some crazy old man and never do what I'm going to say, but here it goes.
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Kog is a mid laner, build him like Kayle (not AD you pleb) and you will absolutely shit yourself over how awesome he is once you get past the HARSH learning curve.
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Go jungle and start golems. Try to first back devourer. Skill order is WQE.
Try those a couple times and see what you think. Sorry to not give you a satisfying answer, but Kog has been a shit ADC since they removed Bloodrazors. Don't let anyone tell you different.