The problem with Gnar is obvious...
Gnar has been out almost 2 weeks now and still has a 41% win rate (lower in higher ranks). Looking at the buffs, Riot still seems clueless as to why. A big clue to his core problem is that currently, the only people having success with Gnar are people who build him pure tank (which isn't how most people want to build him, as it's not as fun).
Why is pure tank the only viable role? Why does he feed if he builds almost any damage?
Because Gnar's defensive scaling (the worst in the game) combined with his range (the worst for a ranged champion in the game) is just plain ridiculous and fundamentally doesn't work on a champion.
If by chance you don't believe me, lets put things in perspective, shall we? Here is Mini-Gnar's base defensive stats at level 18:
Mini-Gnar at Level 18 1600 HP 64 Armor 485 Range (400 at level 1)
Now, lets take a few characters like Caitlyn and Graves for a counter example. Caitlyn has significantly more range, a trap-based root, and a good escape with her net. She is a MUCH, MUCH safer champion than Gnar. As a shorter ranged ADC, Riot thought Graves would need slightly better defensive stats to make him viable, so he should compare better with Gnar. And yet, here are their level 18 stats:
Caitlyn at Level 18 1830 HP 80 Armor 650 Range
Graves at Level 18 1922 HP 76.6 to 106.6 Armor (depending on his passive stacks) 525 range
Significantly more than Gnar! Why? How does this make sense? Are you starting to understand why Gnar sucks?
BUT WAIT! THERE'S MORE! Gnar and Caitlyn are not really comparable. Gnar was designed to be a top lane bruiser, not an ADC! So, lets take a look at a few champions that are more similar: Kayle, Nidalee, and Jayce.
These champions are top-laners/mid-laners. They also swap between ranged and melee modes like Gnar (almost at will, unlike Gnar). They all have longer range, are all highly mobile, and have better tools to stay alive as well (i.e. Nid and Kayle's heal, Jayce's hammer disengage, Nid's uncatchable cougar form, etc.).
And yet, here are their stats at level 18:
Jayce at Level 18 2040 HP 93 Armor 500 Range
Kayle at Level 18 2092 HP 84 Armor 525 Range
Nidalee at Level 18 2010 HP 93 Armor 525 Range
HOW DOES THIS MAKE ANY SENSE? NOW DO YOU SEE WHY GNAR SUCKS? He literally can't get in range to do damage without being bursted!
And how am I supposed to fight another lane bully like Nidalee or Jayce when they not only have hard engage, but they are significantly tankier than me for no reason? I have to drastically outplay them for no other reason than they can out trade me even if I hit them more! Even funnier, despite having much lower defensive stats, Gnar also has much lower AD at 18 than every one of these champions, including Caitlyn!
Riot, this is just plain ridiculous. There is literally no reason for this gross lack of stats on Mini-Gnar. Gnar will never be viable as anything other than a pure tank unless you either give him much better defensive stats or longer range. It's just a fundamental truth to the game.
If you really want to keep him similar for some reason, here's a suggestion: how about giving him increased range that scales with his bonus AD/AP? You could also give Mega-Gnar increased speed and possibly jump length that scales with his bonus AD/AP, allowing him to be safer and not get blown up as a carry.
TL;DR: Gnar's core problem is his ridiculous and inexplicable defensive scaling combined with his range - which most people don't realize how ridiculous it is. He has significantly lower health, armor, range, sustain, and escape than any other similar champion in the game, such as Jayce, Nidalee, Kayle, and even much longer ranged, safer ADC's like Caitlyn (see above for the shocking numbers). A champion like this fundamentally cannot work because the moment he gets in range to do damage, he can be instantly bursted. This is why the only people currently having success with Gnar build full tank. Riot must buff his defensive stats to make damage builds viable or make his mini-gnar range and possibly mega-gnar speed scale with bonus AD/AP.