The original concept of him being a fighter is fine, but he has too much utility. Gragas has naturally beef with his passive and W, which are all fine and dandy. However, we need to look at what defines the roles. Bruisers and Tanks both bring beefiness to the game, but their secondary goals diverge based on their kit.
Does the kit have high utility or CC? If yes, then the champion is better off as a tank, regardless of the dps.
Both tanks and bruisers have the goals of soaking damage. That's why a champion like Mundo (who /is/ a tank for all reasoning) is actually a bruiser since he has only 1 soft CC, a slow, and no other utility. Similar to someone like Darius who has a melee-range slow and a short-range grab (however this can be argued since his slow is so immense...leading to controversy of his Utility/DPS ratios). Gragas has three CC spells; this qualifies him as a tank since he is a damage soak with crowd control. Thus, you need to specify him as either a bruiser or a tank. Since he has the CC spells that automatically qualify him as a tank, only changing his kit entirely would allow higher damage values and giving him the label of a bruiser. Thus, his dps needs to be nerfed to make him more fair as he is already an excellent tank.
Does that help explain things?
EDIT: On your latter point of "Another thing I wanted to add is when an AP Fighter wants to build AP and HP they just seems to be squishy."
The issues arise that most AP champions are designed for dps and utility (either in mobility/CC/or both), which are the core building blocks for mages. Now, we must look at why they're so squishy: they don't have any innate tankiness. Since mages are at their core DPS+Utility, adding in the option to be tanky, as well, would bring them into the trouble spot we're seeing now with Gragas. They would have Soak+Utility, the building blocks for tanks, but they would also have high dps, which is why tanks were so good for so long. If the dps of hard tanks matches that of bruisers, then why would we ever have bruisers in the first place and not just have hard tanks all the time? That's why the "League of Tanks" was so rampant with Cinderhulk: Cinderhulk enabled high tankiness with cheap dps. While nice, it broke the balance. That's why we don't see AP bruisers. Almost all AP champs have high DPS+Utility, meaning that we can't also give them the option to be tanky, as well. Probably the closest thing we have to an AP bruiser is actually Dr. Mundo, despite have little AP scaling.