Facebook counter not working

I noticed though that the Facebook counter doesnt work..

The number of Facebook Shares our plugin displays is number of times the link of that webpage has been shared on Facebook (i.e. number of times people have shared that on their timeline)
On your Facebook post the number of shares (6) is the number of times people have shared your Facebook post (not the webpage link, saw the difference?)
You can see that the official Facebook API for share count is also returning the 4 shares https://graph.facebook.com/https://www.fabionodariphoto.com/wrp/en/luoping-yunnan-china/

Thanks for the clarification. Does that include only shares or also likes?

It includes shares and likes, both.