The Houthis are a large group controlling a big area of Yemen, but not the official government of Yemen. So if the Houthis enter a conflict, that’s not the same as the government of Yemen doing so. But Israel is trying to equate the two. They’re basically saying “Yemeni government, we hold you responsible, we think the Houthis are your proxy.”

So this accusation is not so much about the mere act of entering the conflict, itself, and more about WHO has actually entered it.

A comparison might be if Hezbollah carries out an attack, that’s not necessarily the recognized Lebanese government doing it. But Israel will blame them anyway, if for not other reason than to accuse them of not doing enough to stop it. This comparison is quite apt because both Hezbollah and the Houthis are well aligned with and funded by Iran.