I have been working with some unique material from the Carpathian Basin which show similarities with the abstract decoration of the gaming boards of Ur but I cannot find any publication on these abstract decorations.
You can find some data in I. L. Finkel (ed.), 'Ancient Board Games in Perspective: Papers from the 1990 British Museum colloquium with additional contributions', London (British Museum Press), 2008.
Some other references of interest (especially on its archaeological context) are on the website of the British Museum: http://www.britishmuseum.org/explore/highlights/highlight_objects/me/t/the_royal_game_of_ur.aspx
Thank you so much for your information! I have already got in contact with dr. Finkel and received his papers. Although they are also essential, unfortunately do not say anything in relation to the abstract decoration. I have also found a paper on the figurative (combat like) motifs but nothing about the abstract decoration. Unfortunately neither the general browsing in the internet nor in archives such as JSTOR etc. give valuable information to this theme. There might be some relation to Bactria-Margiana compartmented seals, but they are younger. So, I have to continue seeking.