Question:

Is there way to place the play button not in the middle, but in some other place on the video?

Answer:

Yes. In step 3, Options tab, click the Advanced Option button, then enter the following CSS code to the Custom CSS:

.amazingcarousel-play-video {
    background-position: bottom left !important;
}

This will move the play video button to the bottom left.

A demo is as following: