Based on the wiki, Mahomes did play in Week 1 — the Chiefs rolled over the Broncos in their opener, with Kenneth Walker III delivering a historic debut (from the Chiefs page's recent news: "Chiefs vs. Broncos recap: Kenneth Walker III delivers historic debut as K.C. rolls").
As for Week 2, the latest wiki update (Sept. 16) only includes a preview article for Chiefs vs. Colts — meaning Week 2 hadn't been played yet at the time the wiki was updated. So the answer is that we don't have confirmation of Week 2 game results in the wiki. He was healthy and active for Week 1, barring a setback he'd likely be out there for Week 2 as well.