I suspect that the suicide shouldn't be included crowd is right, but for a different reason than they think. It's quite simply not defined as homicide. Suicide by whatever means, is mostly about the availability of that means. IMO, overall rates of suicide wouldn't change even if you removed all firearms from the planet and hurled them into the sun.
But that isn't the point I was trying to make here. I was making a point about statistical sources. If you cherry pick statistics, you can find criteria that will fit almost any model you want. The author of the report you linked to, is a guy named John Lott. He is an economist, who is therefore incredibly well versed in the manipulation of statistics. My opinion of him is that he is also a biased reporter, who has a vested interest in the specific statistics he reports, since he has written several books that sell very very well into the Second Amendment crowd. He would lose his income if he didn't spin the numbers the way he does.
But If you're looking to learn the scope of mass shootings, then look at mass shootings, set a simple definition that does not exclude mass shootings. The accepted definition seems to be, "Firearm discharge involving the injury or death of 4 or more individuals". It's not an official definition, it's just that is the most often cited definition and it seems reasonable to me. If you go on to exclude cases where no other crime was committed, you exclude exactly the kind of thing you would want to look at - namely, how big is the problem? Why is that? Because what constitutes a crime varies from jurisdiction to jurisdiction. That makes it very hard to make a fair comparison. This is true even if you just look at the US and ignore the rest of the world. There are 51 Governments in the USA, (counting Federal) and what constitutes a crime in each, is different.
