Yes this item plays HD youtube videos.
Again, please excuse my first response and disregard as I didn't catch the "HD" part of your question.
You'll have to spend a bit more if you want to watch HD video on a smartphone. Phones in the price range generally do not have HD quality display capabilities.
I was just answering assuming you wanted to watch normal YouTube and having the faster data speeds that the Unico will give would be better than the choppiness and waiting for buffering that 3G speeds will sometimes have a tendency to do depending on location, time of day, tower congestion, etc. I'm using a 3G smartphone now and that happens when I watch YouTube. YouTube on 4G LTE is generally pretty seamless and smooth.
Sorry about the bad advice.
My advice, and hopefully Jarryed will chime in and probably agree, is to spend the extra $20 and go with the ZTE Unico for $199.88 (copy-and-paste):
The reasoning is that the ZTE Unico is capable of receiving 4G LTE will be much better at streaming YouTube videos when it's in an area of LTE coverage. This phone, the Majesty, is limited to 3G data speeds as is the Centura. YouTube with this phone and the Centura will be doable but you may experience some lag and annoying buffering.
4G-LTE will have much higher speeds and lower-latency than 3G and will make a substantial difference in my opinion and experience.
This phone does not play HD video. I also regret to inform you that the Centura also will not play HD video.
Neither screen on these phones is HD capable.
You will need a minimum screen resolution 1280 x 720.