The filament is heated by electrical resistance. That heat energy comes out as photons in a wide band in the visible and infrared parts of the spectrum. Some of those photons are intercepted by the glass bulb, the metal housing, etc.; their energy heats these materials up.

Even though a vacuum prevents conduction of heat energy, it doesn’t prevent radiation of that energy in the form of photons. That’s how the light gets from the filament to the room; and that’s how the heat gets to the surface of the bulb too.