yup, that common, although most are folk-arts rather than military (jujitsu, pankration, & sambo being the first military grappling styles to come to mind).
you have bok in mongolia, glima in iceland, backwrestling in ireland, highland wrestling in scotland, greco-roman from the obvious, ssireum from korea, pehlwani from persia, lancashire wrestling in england. sambo is rooted it judo & styles from about six other countries including georgia, armenia, & uzbekistan. one of my students was in the peace corps in west africa & told me about some sort of harness wrestling there, though he didn't remember the name. then there is sumo, judo, freestyle, collegiate...all the familiar ones. so it is pretty common in other nations.
clearly, being on the ground in the battlefield is not a great position. however, there was evidently a need for it in some cultures or else it wouldn't have developed. i did not know that chinese warfare was conducted as you said; it sounds like formation fighting was pretty highly developed there & that going to the ground would probably mean getting trampled before anyone even had to bother to kill you.
rome & greece also praticed highly disciplined formations during battle BUT single combat challenges on the battle field were not uncommon, which may explain why pankration & greco-roman were still utilized.
if you look some of the medieval fencing manuals, wrestling techniques are included. once again, they are typically in the context of one-on-one, armoured combat, since duels & tournaments were fought in full armour.
anyway, the initial statement that i took issue with is that striking/grappling followed an urban/rural division. it appears to me that grappling as a military art developed in regions where one-on-one armoured combat was likely to take place. since combat on the battlefield was strictly formational as you say, & one-on-one combat was typically unarmoured (making striking more effective), this may explain why groundfighting was never emphasized in china.
thoughts?
jf