I purchased a DSR 2016 4 months ago....and the date on the DOT tire is 3314, 33 is the week and 14 the year.
Should I be concern that I bought it new (The motorcycle) with almost 3 yrs old tires? If I call the dealership where I bought it, should they replace them for newer tires or not?
I don't ride a lot... and most of the info that I found suggest that don't use tires that are 5 yrs old.
To answer your first question/concern: A 2016 (model year) vehicle was very likely built in 2015, using parts the manufacturer had before then. As Richard230 explained; the tire itself would have been manufactured up to a year prior to the motorcycle manufacturer's receipt. And after the tire is put on the vehicle it still needs to be shipped/purchased before any consumer ever gets a hold of it. So, the youngest tire I'd expect to see on a new 2016 vehicle would have been made late 2014.
And I think that answers your second question; You have a "new" tire that's about as young as original tires on a 2016 (MY) could be. If dealers were expected to replace tires that are more than about a year old they would have to replace the tires on every new vehicle.
As for the overall concern of a tire's age: You can usually see tire wear. But even without bothering to inspect the tire for wear: If a tire has been stored in a cool-dark-dry place for ~10 years it should still have a full life ahead of it (assuming excessive use within a year or two). I wouldn't buy a tire over 10 years old, even though it could be ok. 10 years is a common limit put forth by tire manufacturers, but keep in mind that they air (err) on the side of extreme caution, probably considering high-end performance.