My reading of this is that base-to-base contact is what defines engagement and, once in contact, figures are constrained in what they can do. In the case of a character charging an enemy, I take this to mean that both the character and the enemy are now engaged.Move: Rules for movement are given in the section on Moving. If this brings characters into base-to-base contact with an enemy, they are engaged, and may only follow the move with the combat or flee combat options.
What about the scenario where moving a figure ends in base-to-base contact with multiple enemies? If a figure charges an enemy and that puts them in base-to-base contact with two enemy figures, are all three figures engaged in melee? If so, does it matter that the character could only attack a single enemy?
To put a finer point on it, does engagement require that a melee blow is at least attempted between two figures or is it simply a case of adjacency? In the scenario where one model moves into contact with two enemies and attacks just one enemy, when the enemies move are both of them only allowed to attack or flee? Or just the enemy that received an attack?