I don't think the player was infringing the spirit of the law in this case because he was promptly running to leave the FOP
I think this Law change would've been better if it had given the referee the option to insist that the player departed at the nearest point. The existing Law change is unmanageable and unnecessary for most us
The law states; 'the player must leave at the nearest point unless the referee indicates otherwise'. I would say he is still infringing even the spirit of the law simply because it would have been quicker for the player to run to the far touchline to get off the pitch even more quickly. Your comparison between simply walking and running is not the comparison to make. The law mandates a 'must'. The referee didn't indicate otherwise. This player clearly showed a lack of respect for the law and the referee.
Of course, in youth and park games, this law, as with several others, won't be brought into play by the referee.