A link that has come up in a couple of discussions is this http://jesperhansen.co.uk/play/ that tells the difference between 'lege' and 'spille'
I am sorry I cannot remember the name of the person that posted it first (think it is a dutch law student) otherwise I would have written your name to give you credit for the link - I am just a copycat of your very very good link.
In a different thread on here, someone aptly states that:
Leger is to play outside (running, jumping, yelling) and Spiller is more structured (i.e. Board games, chess, monopoly etc.)