I, too, am very surprised he's not been included for the Slovakia match. Not that I think he's been playing as well as MC11, hafnia, and others say, but because several of the other midfielders don't impress much.
As to the substantive issue of his strengths and weaknesses, I'll hold up my hand as one who does tend to focus more on his flaws than his positive play, and so might be "picking on" him too much and not "taking note of what he's doing."
What I see him doing, way too often, is trying to dribble past multiple defenders near and in the box, foolishly and repeatedly hoping nearly to dribble the ball into the net, rather than blasting it. Second, too often -- not always but too often -- pirouetting between 2 defenders or reversing direction and losing the ball. Koeman commented a few weeks back on this latter tendency, and said they are working on this problem. What MC11 describes as "giving the team a chance to reshape and have a breather," I see as slowing potential attacks and missing shot opportunities for himself and others.
I see Barkley's marvelous abilities and so assume his strengths will become more apparent (even) to me, as he displays them more consistently. And perhaps I am simply wrong about the weaknesses.