Was the Muggle attack on Ariana Dumbledore sexual in nature? When I read this, I noticed a lot of "hand-waving language", typical in situations when the author wants to keep the book family suitable but is alluding to something sexual.
First I would like to correct that it was not Dumbledore who informed the trio about Ariana’s fate, but Aberforth at the Hog's Head after saving them from the trap in Hogsmeade.
I disagree with Slytherincess. Aberforth said "trying to stop the little freak doing it", not punishing her for it; sexually assaulting her is not directly linked to stopping her magic. While the exact age of the attackers is not given I presume they were still before puberty so this is again unlikely to be a sexual assault.
J.K.Rowling did not state the exact reason because it seems to be horrible enough and leave the imagination to the readers. My logical conclusion was
given the historical background (which Rowling used extensively in the books), that Ariana was undoubtedly a witch, and that the boys got carried away to stop her: They tried to burn her alive. Ariana survived because we know wizards and witches are much more resilient to normal damage than Muggles and magical cures are much more powerful. But naturally it broke her completely and was a sufficient reason for the father to hunt down the boys.
It's obviously not explicitly stated, as you note, and J.K. Rowling has not addressed this specific question in any interview I'm aware of (perhaps someone else knows of one?). I will say that the impression I came away with after reading about the attack on Ariana was that she may indeed have been sexually assaulted, or that at the very least the attack might have involved some improper language and/or perhaps touching.
Ariana was so traumatized that sexual assault seems possible; of course, that level of trauma can certainly result from a purely physical attack. I would say that it would seem more likely that a little girl's father would actually attack the juvenile offenders if sexual assault were involved.
ETA: I stand corrected. Thanks to Anthony Grist, I went back and re-read parts of Deathly Hallows and discovered that Dumbledore's father attacked the boys who attacked Ariana; there is no indication he killed them:
‘And my father went after the bastards that did it,’ said Aberforth, ‘and attacked them. And they locked him up in Azkaban for it. He never said why he’d done it, because if the Ministry had known what Ariana had become, she’d have been locked up in St Mungo’s for good. They’d have seen her as a serious threat to the International Statute of Secrecy, unbalanced like she was, with magic exploding out of her at moments when she couldn’t keep it in any longer.
‘We had to keep her safe, and quiet. We moved house, put it about she was ill, and my mother looked after her, and tried to keep her calm and happy.'
Deathly Hallows - page 455 - Bloomsbury - chapter twenty-eight, The Missing Mirror
So I've tweaked this answer accordingly, to reflect an attack on Ariana's abusers, rather than their being murdered. If you want to see the differences between the two answers, just check the edit history. Basically, I've reversed my stance on the attack "obviously" having been sexual in nature to possibly having been sexual in nature. For it is possibly. But from the canon we have, a definitive conclusion can't be drawn.
As well, Dumbledore, at one point in his life, advocated wizarding subjugation of Muggles, a decidedly anti-Muggle stance. Perhaps his father had anti-Muggle leanings as well -- and planted the seed in Dumbledore's mind that Muggles were inferior to wizards -- and this made it easier for him to attack the Muggle boys. A total guess on my part, because Mr. Dumbledore never made a confession.
So, there is no absolute canon answer to this question, but this is what I have concluded.
Feel free to retract your vote if you feel uncomfortable with my reassessment.