The most likely answer for what is going on here is the one right on the surface. Prigozhin realized that he could try to take Moscow, but he'd ultimately be defeated, Putin was already gone. He acted without any political support and without having a bunch of aces up your sleeve an attempted coup is destined to fail. It would also drag units away from Ukraine to deal with him and undermine Russian efforts in the face of the Ukrainian offensive. Prigozhin is still fighting against Ukraine and probably recognized that he would go down in Russian history as a traitor. It was very likely just a rash miscalculation by Prigozhin. He's hoping to use this as political leverage now, but my guess would be that he winds up dead pretty soon. I doubt there's any 4 dimensional chess going on.

If this is the case, then this isn't going to be the Russian Civil War/Coup that people had hoped to end the war. Russia is certainly a mess though, and this might cause other political forces in Russia to act.