It begins with "her husband was handcuffed, tortured, and killed inside her house," which obviously is not accurate.
As far as the COD, it looks like they quoted the ME's findings as "Airway obstruction as a result of suffocation," and the rest is speculation. I doubt the ME said "the killer allegedly closed the girl's mouth with pieces of cloth, pushing them unbearably and squeezing them with the palm of his hands. In fact, the stubborn criminal blocked her nose."
They may have found cloth in her mouth so they know she was gagged. She died from suffocation due to airway obstruction (asphyxiation) but we don't know exactly how. The perp could have used his hands or a blanket or a pillow.
They go on to say that "the authorities have in their hands a video with a suspicious man, who at 5:30 in the early hours of Tuesday is outside the house." They say that it has not been excluded that the robbers had an accomplice, who was guarding chilies and possibly informed him as to whether to stay or leave the house.
Police estimate that the family had been the target of the perpetrators for a long time and that they knew the movements of both the 32 year old and his wife. The three perpetrators, according to the experience of the experienced officers of the ELA's, are most likely marked by a rich criminal past.
They also say there was only one camera inside "which the perps located and turned to where he was looking so as not to be seen." Also, "When police arrived, they found the external security camera damaged."
I've read similar details in other articles. Has all this been discounted by LE?