There's no 'may' about it mate, it's fact.
See for yourself, deaths by terrorism these year via Wikipedia:
https://en.m.wikipedia.org/wiki/List_of_terrorist_incidents,_2015
Also, I never added a prefix that it was "Islam vs the rest", only that it was violence with a religious motivation. Of which Islam is responsible for the most deaths, this isn't disputable. And yes, most of those deaths will be Muslims killing other Muslims. Still a problem - no?
True. But it's 2015AD. We're talking about the present. This all too often serves as a whataboutism for people to gloss over the reality of the scale of this religious violence in the present day. You're right to point out that the separation of church and state is something that was key to Christianity's moderation, but how far are we really from seeing that become more commonplace in the wider Middle East? Especially when this seems to be in direct opposition to many Muslims' beliefs that man made laws are unworthy when there is Sharia, God's law, as per the Koran?
This regression into deeply religious social conservatism is what seems to be culpable for a lot of the violence.
No one is implying that the violence is taking place because Muslims are inherently violent. They're not being violent because they're Muslim.
The violence is often motivated by religious belief however, this is inescapable. Religion often goes hand in hand with a political goal. They often meet nicely to serve one another.
None of the groups you highlighted are secular groups, religion is central to their goal, it runs parallel to their political goal.
They're all divided along sectarian lines also. And thus their religious beliefs differ, and their political goals, this is no coincidence.