I saw this graph, and others much like it, frequently on social media. I think is is a good idea to look into things that seem contrary to your impressions, and this one seemed to challenge mine.
As a engineer, I also always like to look at the source data, so I sought out the article from the New America Foundation, Terrorism in America, that was cited. The graph below appears in the article, and sure enough, it looks like the one above, with a big spike for Jihadist victims in 2016, since the dataset has been updated since the previous chart was generated. You can download a set of .csv files from the New America Foundation that contains all of the data they have collected. I appreciate the effort that went into compiling this, and I also appreciate the New America foundation and the authors choosing to share their data freely.
Looking at that data set [downloaded 2016-12-19], I was a little surprised at what I found. Looking at American domestic attacks only [Mumbai is a big spike in 2008], out of 210 plots, 190 had been categorized as Jihadist, as compared to 19 Right Wing and 1 Left Wing.[and one with no data, the 2010 King Salmon plot] That is an order of magnitude of difference between all three categories!
I decided to plot the data in a number of different ways, which is often a good way of looking at trends in a dataset. I excluded anything outside of the US [foreign_attack=TRUE in the dataset]. I also just summed victims by year, rather than using a cumulative sum like the New America Foundation chart. Here are my charts:
One of the biggest differences is how often a given plot is prevented. Jihadist plots are prevented much more frequently than right wing plots. In the chart of prevented/not prevented, deadly attacks are not included. You can see that in the next chart down, which compares plots per year to the number of people injured or killed. I've said before that we are lucky that our enemies are so incompetent. Here is proof it is true.
The big differences are in rate of occurrence, and in rate of prevention. I don't know enough to really understand why the FBI and other American police forces and security agencies are so much better at preventing Jihadist plots than right-wing ones, but I think that given the 10x difference in rate of plots, they are doing the right thing.
By the way, I think my initial impressions ended up justified by the data.