First of all, your definition of missile is not correct.

By its very definition, a missile is something that is thrown. Even a stone or arrow can be a missile by definition if it is thrown. Therefore, what you are describing is also technically a "missile" (1/2) https://twitter.com/adhy_sv/status/1386104271943262208

Then, according to Eminent Karnataka historian Sūryanātha Kāmat , this sculpture depicts a rocket.

Rocket here means an arrow whose tip was dipped with gunpowder. And it was then fired at the enemy. (2/2)

In fact, the English word rocket is borrowed from Italian word "Rochetta".

The word was used to describe an arrow dipped with gun powder. This is exactly identical to the "rocket" that was shown in the Hoysala sculpture

http://abyss.uoregon.edu/~js/space/lectures/lec01.html