Do I need a visa for Russia if just transit through Moscow?

Yes, you do. From Transit visas:

The following situations do not require a transit visa:

• Foreign nationals flying over the territory of the Russian Federation without changing flights in the country;

• Foreign nationals flying with an international airline and changing flights in the Russian Federation, at the same airport on both the outward journey and the inbound journey (on condition that this airport has a transit area), in possession of properly completed documents confirming their right to enter the destination country, and an airline ticket with a confirmed departure date from the airport in Russia where they changed flights, no more than 24 hours after their arrival date.

The second part applies to you, however, it goes on to say:

Please note that if a foreign citizen travels across the territory of Russia to the countries of the Customs Union (Belorussia, Kazakhstan, Armenia, Kyrgyzstan) he is required to apply for a transit visa, unless he’s a citizen of countries eligible for visa-free travel to Russia in accordance with bilateral agreements.

Since you are going to Kazakhstan, which is within the Customs Union, you are required to have a transit visa. (US citizens definitely are not eligible for visa-free travel to Russia itself.)