It's true that Lubriplate was selected by the US Army as the lubricant of choice for the M1 rifle before WWII. It's selection was based on the ability to lubricate high friction areas (operating handle cam, bolt lug, etc) and resist being washed off during heavy rainstorms. It was a translucent, medium dark, gooey grease.
That MIL-G specification you listed was developed during the middle 1950's when the US Military went to procurement specifications for lubricants, oils, and solvents. It's intended for all small arms use, including the M1 and M14 rifles, BAR, M1919, M73, M60, and M1/M2 .50 cal machine guns. As a product formulated to meet specifications, the appearance will vary. I've seen light and dark amber, yellow, translucent, and creamy greases using that same MIL-G
It's not cosmoline. I believe cosmoline was eventually listed under a MIL-P (preservative) specification.