For me the required characteristics would be that it dispenses a burning liquid at a distance in a controlled, directed manner.
If it dispenses burning gas it’s not very useful as a weapon and is really just a big gas burner. Roofing torches, blowtorches, and weed burners fall into this category.
If it doesn’t cover a meaningful distance it’s also not very useful as a weapon and is essentially just a leaky container. Driptorches fall into this category.
If it dispenses the burning material in an uncontrolled or undirected manner it’s either an incendiary bomb/grenade of some sort or an accident. It might be a weapon but not one I’d call a flamethrower.
For me the required characteristics would be that it dispenses a burning liquid at a distance in a controlled, directed manner.