I typically only hear of the term “flamethrower” in a weapons context so yes, I’d say that it has to be a weapon. Yes, you can have a noncombat device that projects a flame but those are typically called something else (like “burner” or “torch”). I’d expect most people to first think of a weapon when they hear “flamethrower”.

And I would assume that your device’s flame is still controlled and directed – it may have some spread but you still choose where to point the device even when it’s active. You probably also have a means of turning the device off, offering further control. So your device fits the definition, even if it might be crude.

An incendiary grenade would be an example of a device that offers no control or direction. Once it goes off it releases all the fire everywhere within range. Another example would be a burning gas well – it might project its fire in a fairly predictable fashion and in a clear direction (up) but you can’t easily turn it off or point it somewhere else.