For a finite-dimensional simple Lie algebra $\mathfrak{g}$ admitting a non-trivial minuscule representation and a connected marked surface $Σ$ with at least two marked points and no punctures, we prove that the cluster algebra $\mathscr{A}_{\mathfrak{g},Σ}$ associated with the pair $(\mathfrak{g},Σ)$ coincides with the upper cluster algebra $\mathscr{U}_{\mathfrak{g},Σ}$. The proof is based on the fact that the function ring $\mathcal{O}(\mathcal{A}^\times_{G,Σ})$ of the moduli space of decorated twisted $G$-local systems on $Σ$ is generated by matrix coefficients of Wilson lines introduced in [IO20]. As an application, we prove that the Muller-type skein algebras $\mathscr{S}_{\mathfrak{g}, Σ}[\partial^{-1}]$ [Muller,IY23,IY22] for $\mathfrak{g}=\mathfrak{sl}_2, \mathfrak{sl}_3,$ or $\mathfrak{sp}_4$ are isomorphic to the cluster algebras $\mathscr{A}_{\mathfrak{g}, Σ}$.