I'm no expert but I follow one or two on twitter, and from that I gather that it wasn't really a coup. When they had their Arab Spring, the (unbloody) "solution" was to replace one moustache with another,
and the regime stayed the same incompetent and highly corrupt US puppet. This Houthi group seems to originate in Shi'a tribes but formed to something bigger with relatively broad support at least in the North. Their militias took over the capital Sana'a months ago already. But not the regime; instead they made demands about developing a new federal constitution and following elections. This seems to have made slow progress and they resorted to violence, including arrests/hostage-taking of a presidential adviser. This led to
this "agreement" from Wednesday and the adviser was released as agreed. And now the regime resigned, which was not part of the agreement, apparently to the surprise of the Houthis.