It’s just the usual conflict between rules and narrative that is all over D&D 3.5e. In reality, The Crystal Shard, where the forging was first described, was written in 1988, long before the 3.5e rules were written.1 Aegis-fang doesn’t even have 3.5e stats.
As it turns out, D&D 3.5e is not just poor at emulating all manner of characters from other media (cf. character build for Gandalf in D&D 3.5e), it’s also poor at emulating characters even from its own media. The rules of D&D 3.5e just don’t line up as well as most would like with the narratives that the rulebooks and novels suggest they go with. If you follow the rules strictly and allow them to dictate the narrative setting, what you end up with is the Tippyverse, or maybe Eberron if you include an arbitrary level cap and deus ex machina dragons to keep things in line.
It is a common criticism of Forgotten Realms, for instance, that it has all these epic-level mages holing away in towers doing apparently nothing (because, by the rules, they could solve pretty much any and all problems with barely any effort, because Epic Spellcasting is broken). This is necessary to have a game since it’s not much fun to run to the nearest sympathetic archmage and have them fix it with a wave of their hand, but it causes conflict between the rules and the narrative.
The narrative-rules interactions also have problems in the reverse: the ranger class is largely supposed to let you play as Drizzt Do’Urden, but since he was a bit of a Marty Stu kind of character who could do everything, the ranger class gets a bit of everything at a drastically cut-down rate, and ends up being quite poor at doing any of those things.
So basically, what Bruenor did is not something players can do by the rules. As Ruut mentions, there are ways to create magic items without casting “spells,” and there are ways of upgrading special magic items you already have, but Bruenor wouldn’t have had those. Dungeon Master’s Guide II has rules for bonded magic items, which any character can create and upgrade without needing item-creation feats, spells, or any special crafting class feature, so Bruenor could create a magic item that way, but bonded magic items only function for the person who bonded them; if Bruenor had created Aegis-fang in that way, it would just be a regular adamantine (or cold iron, or maybe both) warhammer for anyone else.
It is worth noting, however, that while Player’s Guide to Faerûn gives his class levels, more books were published after that time. In particular, Races of Stone was printed well after that point. It includes a battlesmith prestige class, which was likely an attempt to provide a class that could be used by Bruenor or someone like him to produce magic weapons like Aegis-fang.
- In fact, not only was this prior to Wizards of the Coast, who wrote 3.5e in 2003, acquiring the D&D license from TSR, this was prior to Wizards of the Coast, which was founded in 1990.