Does Ryanair have the sequential use of flight coupons rule?
Meaning if you miss any flight-segment on your itinerary all subsequent segments are canceled.
Does this rule apply if tickets are bought in one booking?
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Ryanair only sells one-ways or returns so the only case is missing your first flight and still wanting to take the return. That is possible without any actions necessary on your part as stated here on their website FAQ:
You don't need to notify us if you are unable to travel and if you can’t use your outbound flight you can still use your return flight.
So yes, if you miss the first flight you can still take the return flight and no, there is no sequential use of flight coupons rule.
Most low cost airlines, including Ryan Air do sell each flight as individual item. Meaning that if one flight is late, you are not guarantied onward travel even if you have bought your tickets from the same site at the same time.
On the other hand, as each portion of the travel is an individual one way ticket, if you miss one flight but are in the right spot on the right time for your next flight, you can fly, as it is a separate flight.
I hope to add links to this answer, for now I am searching them. No link with proof for the 'individual tickets' yet, but I found one that states that there is a 'missed flight fee' looks like that for 100 euro or 100 pounds they might be willing to book you onto an other flight, which is an improvement over former policies