Brandon Kintzler, at his current pace, will be worth about 0.55 bWAR the rest of that season.
He's very unlikely to be the difference between anything.
It was 0.69 bWAR at the time of the trade. By bWAR, it was a top ~20 relief performance in the AL, not exactly the kind of thing contenders usually trade away. So it would seem most teams value that as potentially difference-making. (Plus, Kintzler has actually out-performed that pace so far by 0.5 bWAR with Washington, which could have made a top 10 relief performance in the AL as of today.)
Also, the difference you are describing -- Kintzler or no Kintzler -- is between standing pat and selling. But the complaint here is that we didn't buy when we had the chance -- we could have added another player at the deadline, plus keep Kintzler. Joe Smith and Anthony Swarzak were cheap and have already posted 0.3 bWAR each for their new teams, for example. And as a bonus, getting Smith would have kept him from Cleveland, or getting Swarzak when the White Sox were ready to deal him (July 26) could have helped mitigate some of the 3 walk-off losses we experienced between that date and the trade deadline.