Full disclosure - I've been a Cardinals fan since I was about 5 years old, so take the rest of the post with that in mind.
For the record, I would have much rather seen the Cards win that in a more traditional manner, but the call is absolutely correct and has to be made. Fortunately, the way MLB writes the rule, there is literally no grey area. Intent does not figure into the call. The runner has the right to a direct path to the next base. Once the ball is past the fielder, he is no longer fielding and cannot impact that path in any way. It does not matter that he didn't have time to get up or move. That also is not considered in the rule. Further, the base path is considered to be three feet to either side of the chalk, which he is clearly in.
The rule is in the game for a reason. In the most extreme case, teams could just field 6 NFL linemen sized guys to stand in the base path in front of home plate and the game becomes Red Rover. Obviously the rule is in place so that people can't purposely hinder a runner. Because you often can't be sure of intent, they removed that from the equation. The fact the people debate whether he threw his legs up on purpose or not (even though it does not matter) is exactly why intent was removed from making the call.
Playing devils advocate - let's say he did throw his legs up in order to slow or trip up the runner. How can you not award the base and just play on? The fact that the rule doesn't give the umps the luxury of deciding that is actually good. Instead of judgement call, it's a black and white rule applied the same way every time.
Now all that being said, obviously STL fans are arguing it's correct and most Boston fans argue it's a bad call. But when you look to the middle - those who aren't heavily invested, the vast majority agree it's the right call. I've not seen a single online write up that doesn't agree with the call that was made. Nobody really likes it, but most agree it was correct.
Boston could easily be up 3-0 in the series if they don't make essentially the same mistake twice. Hold on to the ball there - let your closer close and take it to the 10th. Can't feel sorry for the tough call - they put themselves into a position where it had to be made.