I thought that influence was common knowledge?

Ditto. Especially for Starcraft.

Actually the influences for Starcraft were -- I think -- much broader than those for Warcraft.

Warcraft was heavily inspired by Tolkien and Warhammer, whereas Starcraft drew inspiration from basically every sci-fi series ever made, most particularly the Alien series (compare the Zerg Hydralisk to Giger's Alien) and of course from the art direction of Starship Troopers. But yeah, Warhammer 40K was inspirational too.

The artwork for the two alien races in Starcraft were each redone three separate times. The biggest challenge was that players couldn't easily (and quickly) grok the differences between the various units.

In Warcraft, you look at a lumber mill or barracks, and you have an idea what it is and what it might be used for. In Starcraft the difficulty was that -- upon initially playing the game -- it was tough to tell what any unit or building did for you.

Consequently making game units that looked visually familiar by including known sci-fi elements is useful in that -- when done well -- gives players a clue as to the function of a unit.

Or at least that's what we told ourselves when we ripped elements from other games & movies :)

It was playing warcraft & starcraft that got me into warhammer and warhammer 40k when I was in high school, rather than the other way around. Funny that.

I feel like I've mostly heard about people talking about W40k being influenced by (or "ripping off") Starcraft and not the reverse.

W40k was the primary inspiration for Starcraft (W40k has been around since the 80s), and the company that owned it was in talks with Blizzard for an RTS game based on the IP. However, when that deal fell through, Blizzard expanded their sources of inspiration to include more popular Sci Fi sources, i.e., Aliens. and Starship Troopers.