I think people generally understand that it's a dictatorship, referred to as "the Saudis". Much like actions of ISIS are not indicative of what your average Muslim neighbor is up to.
OK, but you'd presumably take issue if a headline said "The Muslims" rather than "ISIS".
I agree that people generally understand that in this case the headline refers to the Saudi government - but OTOH, this kind of "generalisational" language can perhaps be a form of propaganda, or at least subconsciously change some readers' perception with constant exposure.
That's completely different though. That's like referring to the Israeli government is a headline as "The Israelis" vs "The Jews". They're both overbroad when taken literally, but the former is standard shorthand that is clear from context and the latter strongly suggests that writer has an anti-Semitic motivation.
Saudi's refer specifically to the House of Saud, which is the ruling family of Saudi Arabia, if another family was ruling it would be {insert family name here} Arabia
