I'm guessing the idea is that in GR, the solution for a black hole with charge looks different from one without. So in principle you could infer the charge of a black hole based on the curvature of spacetime.
Also, the reference to “known links between the solutions of Yang-Mills theory and those of gravity” (Y-M equations describing charge and EM field) seems to speculatively imply that charge-related information is encoded in the geometry of spacetime, alongside gravitational effects