In follow-up, some have asked “Why the resistor?”
Please note that Ring requires this resistor only when a traditional bell/chime device is NOT being used:
While I’ve yet to reverse-engineer one, it would appear that the Ring doorbells are designed to be able to function as a direct replacement for a traditional doorbell switch, which simply connects two wires together when pressed.
The recommended resistor is intended to act as a substitute in place of a traditional chime/bell mechanism in this case; without it, Bad Things would be expected to happen to the Ring device and/or the installation the first time somebody rang the bell.
Though on a much smaller scale, omitting the resistor without using a traditional bell/chime would be akin to cutting the cord off one’s toaster, twisting the conductors in the cord together, and plugging the cord into a live outlet. A stout spark and a tripped breaker/blown fuse is about the least unpleasant outcome one can expect from doing that… Similarly, omitting the recommended resistor when required is likely to cause permanent damage to one’s new $200 doorbell.