The chiming repeater does not X differently from the minute repeater
The sentence is saying the chiming repeater and the minute repeater each do X in the same way, where X is:
signal the minutes and the quarter hours strike
The sentence is literally saying there is no difference between how the two repeaters do X.
Though this is a bad sentence. The sentence could be interpreted this way:
The chiming repeater does not signal the minutes
the quarter hours strike differently from the minute repeater.
I'm assuming this is not the case since there is no comma after minutes, but it could still mean either thing as written.
EDIT: Thinking about it, strike isn't overly commonly used as a noun, so maybe this second interpretation should be assumed correct. It's a really bad sentence.