One rule the group I play with has been using is that Craft/Strength experience is awarded for defeating ANY encounter which requires you to roll for combat. So, for instance, when randomly encountering in the Crags, Woods, Cave etc. and fighting the mentioned beast, players still receive that amount of Strength/Craft just as if they had a card with that amount on it.
We've also been doing the same for players, up until the last game we played in which we quickly realized this made the Assassin hugely powerful and able to level up like once per turn just by freely stabbing whoever was within range.
So, do you award experience for killing random, non-card encounters?
Players?