I've always been wondering: Do fine cigars such as these have an expiry date?
Well, no and yes.
No in that in the same fashion as wine, both being biological materials undergoing a fermenting type process, the complexity and flavor of a cigar will change over time, and generally improve with age. Yes in that, also like wine, a cigar will reach a peak where it's developed as much as it's going to and begins to degrade. That point is decades into the lifespan of a cigar, with no way to predict when that might be other than just smoking one of your old cigars every now and then and seeing how they taste. So I guess you could call that peak the expiration date, but not really in the same sense as the date you find on the milk carton.
People age cigars all the time, and often have quite extensive collections in the same way that wine drinkers will have a cellar full of bottles from many different years.