I suppose it is a moot point as to whether the Russian invasion and devastation of Chechyna is politically motivated, i.e. to defend the integrity of the Russian Federation, or a resource war in the sense that Chechnya is critically located in regard to the access to central Asian oil and gas.
Bearing in mind that Yeltsin had just smashed the USSR, and that there was a real danger of the Russian federation exploding, I don't see why you'd need to look for complicated explanations. He thought that by coming down hard on the Chechens, he'd put the fear of God in the other potential breakaways. It actually worked, except for the Chechens.

After the fact, you can graft on whatever other motives you want. Religion, resources. And they end up coming true.