"Gunpowder Empire" is not a term referring to any empire which utilised gunpowder and gunpowder weaponry; it is an informal term used specifically for Marshall Hodgson's conception of the type of empires which existed in the Middle East during "gunpowder times", as he phrased it. Specifically, Hodgson conceived of the Ottomans, Safavids and Mughals as a modification of a Mongol/post-Mongol "ideal" of a military-patronage state (defined as a state proceeding from a Mongol tradition, and specifically containing secular imperial laws alongside the shar'ia, a state envisioned as a solely military enterprise and with all resources suborned to the military elite) combined with a resurgent imperial absolutism, something he thought was only possible due to the military power granted by gunpowder weapons in the late 15th century. The utility of the term is rather contested, especially regarding the role of gunpowder weapons; but either way it is a more specific term used in a more specific context than its name would indicate.

If you want to read more, Hodgson describes his military-patronage state on page 405-6 of the 2nd volume of his masterpiece The Venture of Islam, while he talks more about his conception of a "gunpowder empire" at the beginning of his chapter on the Safavids in the 3rd volume.