For those interested, here is Snopes' take on it:
Snopes says Mixture.
They have no issue with the accuracy of the data; their primary beef is simply that they believe it is misleading. I'm pretty sure that's an opinion, not a fact, but nevertheless...
The first issue they have is with the study's definition of a mass shooting, though they admit there is not a consensus on that point. The study's definition, focusing on public mass shootings, is a shooting involving “four or more people killed in a public place, and not in the course of committing another crime, and not involving struggles over sovereignty.”
The second issue they have is that the study uses the mean rather than the median number of related deaths in a year, making a more significant statistical difference for smaller countries being compared to the much larger population of the United States. Their opinion is that the average number of people murdered in such a way over a period of time is less important than how typical - or how often - these events occur. On the other hand, a median figure is always going to have a larger statistical margin of error for smaller sample sizes - likely putting a larger sample size at a statistical advantage or disadvantage, depending upon whether the median on the smaller sample sizes tends to fall on the positive or negative side of the error.
Basically, they say it's misleading because - while more people per capita were killed in several European countries as compared to in the U.S. over the given time period - most of the European countries in most years experienced no mass shootings over the given time period. On the other hand, the same thing can be said of most of the States in the U.S. - a closer population comparison to most European countries than the U.S. as a whole.