Discontinuous with respect to what? The discount rate just is, and there just is an optimal policy set for each reward function at a given discount rate, and so it doesn’t make sense to talk about discontinuity without having something to govern what it’s discontinuous with respect to. Like, teleportation would be positionally discontinuous with respect to time.
You can talk about other quantities being continuous with respect to change in the discount rate, however, and the paper proves prove the continuity of e.g. POWER and optimality probability with respect to γ∈[0,1].