With 50 games left the Red Sox are only 6 games in the loss column out of the Wild Card. That deficit isn't insurmountable, certainly not given the time the Sox have to close the gap. Even if there are 3 teams the Sox need to leapfrog over while closing that gap.
To use a brutally overused sports cliche, the Sox control their own destiny. Especially since 30 of the 50 games on their remaining schedule are against other teams vying for the AL Wild Card spots.
They play the Athletics 3 times, the Angels 6 times, 9 pivotal games against the Orioles, 6 with the Rays, and 6 against the Blue Jays. If they do well in these 30 games, especially the 9 against Baltimore, then they should make the playoffs.
It's a mixed blessing to face these opponents as it means that the Red Sox will spend most of their last 50 games playing good teams. Apart from these 30 games against Wild Card contenders, they'll play the Yankees 9 times. The only "breaks" for the Sox will be this 4 game series in Cleveland, 4 games against the Royals, and 3 games in Seattle.
I hate the phrase "control their own destiny" so I'll try another way to describe the position the Sox are in: They're responsible. It's on them to beat these Wild Card contenders. They'll have no one to blame but themselves if they fail to beat them.