From my extremely shallow understanding of demography, the proportion of women to men tends to increase with age (in part due to war, crime, and men working more dangerous jobs). Looking at Saudi Arabia and Kuwait as examples, the reverse is true. There are other nearby countries such as Somalia, Iran, and Iraq whose pyramids look much more "normal".
What happened 60 years ago in the gulf to set this off?
The simple answer is those people weren’t born there.
37% of Saudi Arabia’s population is immigrants. Most are not citizens. Some of these are of course religious scholars who have made pilgrimage and settled permanently in the Hejaz, but most are most typical economic migrants. Which is to say, they are mostly prime working age men. Notice that the gender imbalance seems to start in the 20-25 band and peter out after the 60-65 band. In the real core of prime working age—25-45—there are more non-Saudi men in the country than there are Saudi men. Most are from South Asia (India, Pakistan, Bangladesh), with also large populations from other Arab states and the Philippines. There is also a smaller population of highly skilled westerners. Other Gulf Countries are similar. Conversely, you see domestic workers filling these labor demands in larger, more diverse oil rich countries (from Venezuela, Iran, and Egypt one hand to the U.S on the other).
What “happened” wasn’t war but the discovery of oil. While there are many women brought in as guest workers to do domestic work, there are many many more men brought in to work construction, work in the petroleum industry, work in the low wage service sector, etc. These countries also have minuscule female labor market participation and the labor laws in the Gulf States do not allow families to settle permanently and the domestic population has low labor force participation generally. Historically, while “boom towns” in other places draw in male migrants (the sex ratio in the US states of North Dakota and South Dakota are noticeably different because the North Dakota is benefiting from a huge oil boom, but the difference is much smaller than what we see in the Gulf Arab states), these workers traditionally also brought in families and drew women into the labor force. Policy in these Gulf States, coupled with their large labor demand and laws that allow domestic corporations to attain that labor from abroad “on favorable” (often immoral, slave-like) conditions, mean that they have hugely disproportionately foreign male labor forces, to the extent it shows up in population pyramids.