OK. The instrument in the YouTube recording soundtrack is not the instrument in the photo you posted.
The soundtrack features a traditional sounding Irish song and instrument in the soundtrack is an Irish tin whistle (also known as a pennywhistle, an Irish whistle, or sometimes just whistle). They are made in many different keys, but the most common one is a "D" tin whistle.
http://en.wikipedia.org/wiki/Tin_whistle
Here are some other YouTube recordings featuring a tin whistle:
http://www.youtube.com/watch?v=n8ByPLjTQmw
http://www.youtube.com/watch?v=ZDUFtW2KIvY
http://www.youtube.com/watch?v=0tIl0DD0Ta0
http://www.youtube.com/watch?v=CE-fWvL04j0
Inexpensive D tin whistles can be bought for under $10. They are often made of brass and/or various plastics. Really good ones made of wood and silver can cost as much as $500. Here's an example. Do a Google search and you will find them available from many online stores.
http://www.amazon.com/Waltons-Whistle-E ... 0786664509
I have several tin whistles in various keys. They are quite fun to play and easy to take with you anywhere you go.

Generation G Tin Whistle
Generation F Tin Whistle
Generation Eb Tin Whistle
Waltons D Tin Whistle
Waltons C Tin Whistle
Generation Bb Tin Whistle
Clark's 'Meg' D Tin Whistle (Conical bore and plays really sweet)
Shaw D Tin Whistle (COnical bore - Tweaked by Jerry Freeman - also a sweet player)
Homemade D Tin Whistle (I borrow the fipple from my other D whistle)
Chieftain Low D Whistle