From 爆(ばく) (baku-) + 食(く)い (kui, “連(れん)用(よう)形(けい) (ren'yōkei, “stem or continuative form”) of the verb 食(く)う (kū).”). The kui changes to gui as an instance of rendaku (連濁).
ばくぐい • (bakugui) ←ばくぐひ (bakugufi)?