Saudi Arabia fears Iran acquiring another political control point - one on their border at that - in the Middle East and increasingly surrounding Saudi. So they're willing to scorch the earth to stop that.
Also, in terms of territory, with Iran + Persian Gulf, and Yemen + Bab-el-Mandeb straight, you can choke off Saudi Arabia's access to the Arabian Sea. That could heavily cripple their global oil shipping if it came to war, or at least cause a big mess. So Saudi Arabia views having a puppet and or friendly regime in Yemen, to be strategically vital. Saudi has wanted functional pipeline + port access in central Yemen for a long time, to get to the Gulf of Aden, to be able to bypass Iran's territorial waters just in case.
Stalin's quote seems to originate from the 18th century quote which seems to apply as much today as it did then:
One Murder made a Villain, Millions a Hero. — Princes were privileg’d To kill, and numbers sanctified the crime. - 1759, Beilby Porteus, England