I haven't tried this on Playmobil, but it has worked on other plastic items when a stronger chemical doesn't seem like a good idea: mayonnaise. Just regular supermarket mayo in a jar - slather it on, leave it for a while, and clean with soap and water. The only downside I know of is that it may make you crave a BLT.
I think the vinegar in mayonnaise may be the key factor - it may be dissolving the stickiness while the consistency of the mayo holds it in place and, perhaps, makes the process more gentle than vinegar alone. On the other hand, plain vinegar by itself may also work?
I don't have any sticky Playmobil right now so I can't test this out, myself. Whatever you try, good luck!