Hmm, this is the first time I hear of this :(
Could you try doing a cache and cookie clear on your browser to see if this solves the issue? To be quite honest I'm not quite sure what could be causing it, but assure you I will try my best to get to the bottom of it.
It seems it may be caused by the ad as well.
Thanks for your advice but it is not working. I have cleared my cache and cookies but i am still experiencing the same problem.
Do you have any add-ons or extensions installed? If so, which ones?
Could you try disabling it and see if the problem ceases to continue?
Hi Kansha, i'm sorry i'm replying late. I made a mistake with the extensions. The extension/plug-in i have enabled is called "Lyrics Pal" and not "Quick Access Tab". Now i have not disabled it but i cleared the cache and cookies again and now i can move my chess pieces. However, the look of the page is different, everything is smaller, Its almost as if i zoomed out or reduced the size of the page. Here is a picture: 
To get the size back to normal, try moving your cursor in between the chat box and board. A small resize bar should appear, just click and drag to the right to make things bigger :)
From the screenshot i have posted, you can clearly see that i am unable to even see my own chess pieces and i cant scroll down. The banner of the site (the black area on top of the page) also looks way bigger than normal. I have been experiencing this problem for the past week and the problem is not from my laptop because i have not done anything to my laptop that would affect the performance and please keep in mind that i am experiencing this problem only with chess.com's game page.