This would have been a great opportunity to upgrade the cross-platform to include Windows. As a modder it's particularly annoying to deal with multiple versions of the game as the Steam Workshop is shared between the platforms.
The promotion email lets you assume the multiplayer is cross-platform:
We're excited to announce that we've partnered with the team at Feral Interactive to bring Warhammer 40,000: Dawn of War III to Mac and Linux platforms! Feral helped out with the Mac and Linux ports of Dawn of War II and Company of Heroes 2, and we couldn't be happier for them to help bring Dawn of War III to a brand new audience.
Dawn of War III will launch on Mac and Linux in just a few short weeks, on June 8th, 2017. Now all players will be able to do battle as the Space Marines, Eldar, and Orks in an epic campaign, and spectacular multiplayer matches against players around the world.
For more information, check out the FAQ we posted on DawnOfWar.com. For more updates about Dawn of War III, make sure to follow us on social!