Yes, "eki" can be a verb.
"Eku!" by itself is second person imperative so I would only understand it as "You, go!", while "Ek!" could mean that but could also mean "Let's go!" for first person plural (we). You could also say that as "Ni eku!", though.
See also the comment by jxetkubo above.
Could this also be used as a general term to shout when someones procrastinating rather than just "go"
"Come on!" didn't count as right. But really, I think "Ek!" is a word much similar to the German "Los!", the Russian "Давай!" and the Bulgarian "(х)айде!" (which I know is also used in other Balkan countries).
None of those have anything to do with "Going" or moving at all. The English "Come on" doesn't either. So shouldn't it be accepted?