Hello, I'm the author of Embed Chessboard.
I dont have much experience with wordpress plugins, so be patient with me.
First question is: does the plugin actually work (regardless of the warning message)? I'll check, but I might have reduce the amount of warnings displayed by my test site.
Second question: how did you install the plugin? I just deleted and reinstalled the plugin from my test site, using the tools in the "manage
plugins" section of the worpress admin section of my site (so no manual download and ftp, everything done from the admin panel). If you did something different (like manual download and ftp) you might want to try this.
Last suggestion (for now): the "wordpress" part of the plugin has been copied very much from another plugin called "Embed Iframe". First thing to understand what's going on and what's causing the error/conflict would be to follow the instruction of the wordpress.org section of this page to use "Emebd Iframe" and then use it to display chess games.
I would be interested to know if "Embed Iframe" works on your site or if it shows the same warning (good thing is that if the Embed Iframe method works you could actually ditch Embed Chessboard and add your chess games using Embed Iframe, but I should not advertise this too much).
Good luck and thanks for trying the Embed Chessboard plugin!