This is completely false.

Firstly, the Houthis are not recognized as the legitimate rulers of Yemen, so the international community does not grant them the legal right to control Yemen's territorial waters.

Secondly, Yemen does not "straddle" the red sea, as anyone with a passing knowledge of the geography of the area and of what "straddle" means can easily tell. The other side of the strait is Djibouti. Yemen has no rights to determine what shipping can pass through Djibouti waters.

Thirdly, the United Nations Convention of the Law of the Sea anticipated this very thing and added the concept of "transit passage" to the laws of the sea where countries are not to restrict passage in exactly this case, where the only thing that happens is a ship transits from one waters to another through a constrained point. For instance, neither Spain nor Morocco is permitted to restrain shipping through the Strait of Gibraltar.

So, no, you're triply wrong about the legal justification.

Given all the flowery stuff about Yemen and Yemenis, which clearly has taken some effort, to not get the very very basic basics right in your thesis is rather surprising, unless you have some serious ulterior motives, like being paid to advance this peculiarly incorrect viewpoint.