I looked at CSS to see what the width of the div is in which the vids are shown. The art-post div is 458 wide (900 for art-sheet - 2X201 for the 2 sidebars - 2X20 for padding as set on art-post). The width of the LYTE div is set to 640px but also a max-width of 100%, resulting in a width of 458.
The fact that the other plugins are showing a slightly bigger player, is because they don't have a max-width, hence to go outside the box which the content should be in (but as the width of the vid is only slightly bigger it does not look too bad).
Conclusion; although you (the client) prefers the slightly larger player, it does not really honour the CSS.
Possible solution: remove the 2X20px padding on art-post and LYTE player will take that extra width as well.
hope this helps,