You're correct. It's either of the two: they only speak the Russian language or they only speak Russian. Generally speaking, the second option is grammatically incorrect. You can think of Russian as a short form of the Russian language.
Language when used as a mass noun (without an article, that is) means the spoken or written method of human communication. It's visual if we're talking about the written word and aural if we're talking about the spoken word. Here's a simple sentence as an example:
Human language is what we humans use to communicate with each other.
To help you make better sense out of this, think of how it works with the word sound. A sound (or the sound if you're referring to a specific sound) is a particular type of sound that you can make, e.g.: a creaking sound, a screeching sound, a growling sound etc. Sound without an article refers to vibrations that travel through the air or another medium and can be heard when they reach a person's or animal's ear. And here's another sentence as an example:
Sound is the basis for human language. Without sound, there would be no human language as we know it.