Actually, it's attached to value merchants, and so is such as Giant. This is a little clearer if you remove such as Giant, insert a helpful comma, and read it again:
Category killers and niche retailers... are experiencing more difficulty competing with value merchants, with their relentless emphasis on efficiency, cost reduction, and disciplined inventory management.
It's not surprising you had trouble with that, though. That sentence is a monster, and could easily have been broken into two or even four smaller, more easily understood sentences.
Category killers and niche retailers compete effectively with department stores. Those typically have slower inventory turns, high operating expenses, and larger inventory losses. However, they are experiencing more difficulty competing with value merchants such as Giant. Value merchants have a relentless emphasis on efficiency, cost reduction, and disciplined inventory management.