Hi Buffs Mad,
Thank for taking part in our Beta, the feedback we got was really helpful to us!
Good catch, in the Beta version, only 2 icons were shown: Free-kick and Corner-kick Specialists. However, although you probably haven't seen them all yet, in the current animated live match version, you're able to see 8 icons: Playmaker, Penalty-kick Specialist, Penalty-kick Stopper, Free-kick Specialist, Corner-kick Specialist, Defensive Wall, Aerial Defender and Shadow Striker.
To answer your question, note that having players with special abilities definitely has significance. So, you should make sure that you have Specialists in your team to improve your chances to have your players taking the right decision at the right match moment.
Good luck in this season
skyqueen