I learned everything I know about the Granblue Fantasy game from an IRC and the Twitter. It seems like it would be a moderately amusing way to waste time, but I'm mystified at how dedicated some of the players are, particularly those who probably would not self-identify as especially hardcore or committed. It seems as if there is an addictive quality to the gameplay, because when people talk about how they are doing, the representations always seem to be about quantifiable achievements and metrics, instead of how much fun they are having. This (admittedly small) circle of fans seems disinterested in the anime. They are either critical of its quality, or they ignore it entirely because it stars Gran (the male player character) instead of Djeeta (the female player character alternative).
I am watching Granblue Fantasy the Animation with no real understanding of the gameplay or story and only the aforementioned framework as any sort of context. From this vantage, Granblue Fantasy the Animation seems "fine," but isn't particularly captivating. It's a fantasy anime with fantasy-type elements, but these elements are not components of a well-thought-out world, but rather just there because they're just expected to be there or because they make for neat visuals. Just don't be thinking too much about them; it's fine.
As for the characters themselves, again, they are merely adequate or unobjectionable, without really any particular aspect that seems interesting or novel so far. The antagonists who have been introduced through three episodes are all very obviously villainous with cartoonishly evil voices to assist the audience in establishing cursory perspectives about them without having to really pay attention. Maybe Djeeta has something going for her, and the show suffers dramatically from her omission, but—as I understand it—the game plays out exactly the same regardless of whether the player chooses to play as Gran or as Djeeta anyway, so I'm not sure what her presence in the anime might have improved aside from perhaps maybe everything just works so much better because Djeeta is easy on the eyes.
Granblue Fantasy the Animation also competes with Zero kara Hajimeru Mahou no Sho (Grimoire of Zero) and Shuumatsu Nani Shitemasu ka? Isogashii desu ka? Sukutte Moratte Ii desu ka? (WorldEnd: What do you do at the end of the world? Are you busy? Will you save us?) this season, both of which are better shows for the time being. The former has Not Shimakaze explaining the difference between majutsu and mahou (a distinction you may remember from Fate/stay night) and is yet another entry on my list of anime about people who love books, along with Read or Die, R.O.D. the TV, Dantalian no Shoka, and Demonbane. SukaSuka is the adaptation of a light novel and has a super-long title, so I'm pretty dubious about it, but the first episode was reasonably good and non-objectionable, so maybe it has some promise. It's too early to tell how Granblue Fantasy the Animation is going to end up, but it's starting in third place among its peers.