I thought I'd share a piece of code that might come in handy to someone. This is a function that center's the play button inside the video-js player, it works for me. You just need to call it on the pause event and when the player is initialized and not being autoplayed.
Enjoy!
function CenterPlayBT() {
var playBT = $(".vjs-big-play-button");
playBT.css({
left:( (playBT.parent().outerWidth()-playBT.outerWidth())/2 )+"px",
top:( (playBT.parent().outerHeight()-playBT.outerHeight())/2 )+"px"
});
}