I had the same problem, perhaps not quite as extreme as that but the tegiwa solid shifter bushes and short shifter undoubtedly helped a huge amount
It isn't normal no but it does happen. As the plastic parts in the gear stick wear they allow play which then allows the gear stick to move (both side to side and front to back) when in gear. Mine has been like it for well over a year now but is only about 10-15 mm either way. The only real solution is to replace the whole unit (as in the whole gear stick assembly) although there is a thread on another forum about a company who are in the process of making an upgrade kit. Not sure how much that will cure the problem though as from what I have found most of the wear is in the large white ball joint that the whole thing pivots on which is plastic.
Picture don't work homie!
It did work. By the looks of it, it was just a Google picture of an EP3 shortshifter half fitted.