This is muonium: anti-proton plus electron, not muonic hydrogen (proton plus muon). I made the same mistake: it's a very poorly written article.
The role of muon instead of proton could be: (i) to make the bond detectable as the muon decays, or (ii) 10X lighter mass of muonium compared to regular hydrogen leads to a dynamical regime with saddle points in P.E vs K.E (as pointed out earlier).