These guys did neither of those; the Boston marathon has a public gathering but it's not related in any way to politics, wars, Chechnya, religion or anything else. And not only did they not take responsibility, they did the opposite: they ran and had to be tracked down.
An attempt to intimidate? OK, but for intimidate who, from doing what? What's missing here is a message.
I think it's love of killing people, a staple in the human condition, especially among males. Killing or destroying as best you can people you don't like has forever been a major, major motivation and still is, just look at any edition of Google news or any newspapaper. People kill their children, their wives, their neighbors, the police, everybody they can. If they can't kill them, they injure them, banish them, fire them, destroy them emotionally.
Since dynamite was invented, and gunpowder, it's easy to kill lots of strangers, too, so they do. Men love to kill and need little excuse. Wouldn't any of us destroy most of Group X (choose whatever group you hate) if there were a button you could push? What they need is strong government and custom to keep them from killing, and we're
not in a good place that way at this time, obviously.
As for why the Marathon, I note that the older leader -stan guy failed at getting employment and failed at boxing: he just failed all around in what the Marathon runners succeeded at spectacularly. They were pretty much all well off and successful amateur athletes. So he hated them and destroyed them, perhaps, from envy.
Envy. HUGE human motivation to destroy others.