Houthis are not technically the government but they run the nation, they are Zaydi Shias. Zaydis emphasize rebellion against tyranny and follow Imams who do so.

Similarly, Hizb Allah is not the government of Lebanon but they defend Lebanon and carry out its military duties. Because they organized a Jihadist movement with political and military wings and are the de facto armed force of the region.

All state authority generally derives from a monopoly of force. The police operate in territory defended by the military. If an armed force claims a region they are the de facto government of that region.

The Houthi movement runs Sanaa, the capital, so they run the nation. They are technically non state actors.