No, it's not the definition of puppet state. Wikipedia:

> A puppet state is a state that is de jure independent but de facto completely dependent upon an outside power and subject to its orders.

Even though Kazakh president does become dependent on Russian forces to some degree, I don't see how 3000 soldiers can control a country with an army of 100,000, National guard of 32,000 and 86,000 policemen. It may give an upper hand, but against whom? There's even no organized opposition.

If you make paragons Czechoslovakia uprisings in 1968, then USSR sent 500,000 soldiers and 5,000 tanks in a 10 times smaller country.

So it was 3 orders of magnitude larger intervention than this.

Using a military treaty in case of a popular unrest may be illegitimate, but it's nowhere near a puppet state.