Example: Fighter is engaged in melee combat with enemy. Warlock uses eldrich blast with "Repelling Blast" invocation. The enemy is pushed 10 ft. away. Is that creature no longer engaged in combat with the fighter? Would this free movement provoke an attack of opportunity?
No, only a creature's own movement can provoke opportunity attacks (Player's Basic Rules, p. 74):
You also don’t provoke an opportunity attack when you teleport or when someone or something moves you without using your movement, action, or reaction.
Since Repelling Blast is you pushing them and doesn't use their own (re)action or movement, it doesn't trigger an attack of opportunity.