Currently, this site embeds YouTube videos as Flash. (see an example: How to unlock the achievements related to hidden areas in Portal 2?)
However, this is not the best solution, as now YouTube also supports HTML5, and some users (like me!) prefer to use HTML5 player instead of Flash. Supposedly, it should also work on devices that don't have Flash player (I can't confirm because I don't have one).
The solution seems quite simple: just change the embed code to an
iframe, as described at A New Way To Embed YouTube Videos
EDIT: YouTube Embedded Players and Player Parameters says:
<object>embeds were deprecated on January 27, 2015. Please migrate your applications to the
<iframe>embeds, which can intelligently use whichever embedded player – HTML (
<video>) or Flash (
<object>) – the client supports.