No, it's not to do with the right obstructing investigations, although that's part of the overall story. It's the (now former) chief military prosecutor herself, Tomer-Yerushalmi, who is accused of the obstruction of justice.
It's a long and complicated story, but basically: after the abuse happened, indictments were filed against the five soldiers concerned. At the time, the reported abuse was a big incident in the Israeli news; their prosecution is ongoing, but this is not in itself what the current news story is about.
Normally the case would just continue from there in the military justice system. But what happened next was completely unprecedented: far right protestors, including members of Knesset, protested violently against the arrests of the soldiers, and some of them, including a government minister from a far right party in Netanyahu's coalition, broke into military bases as part of their protests and some claimed parliamentary immunity and refused to turn up for questioning. This was seen by most Israelis as a very serious incident undermining the justice system (in the context of a government which has devoted much of its effort to undermining various parts of the justice system). An investigation into this incident is also ongoing, but it's also not what this story is about.
Here begins the current story. At this point, Tomer-Yerushalmi decided to release the video; her explanation in her resignation was that she did so in order to protect the justice system. For whatever reason, she decided to do so by leaking the video to a journalist on Israel's main news channel, rather than using other open channels that were available to her.
And now we get to the current affair: there was an investigation into the leak of the video. Her office declined an outside investigation and conducted an internal investigation, which concluded that it was not possible to find the source of the leak. However, during the last weeks, the source of the leak was discovered to be Tomer-Yerushalmai, and it appears that those in her office doing the investigation knew who was responsible and attempted to cover it up. The cover up included a false affidavit to the Supreme Court, and the mysterious "loss" during the last few weeks of the smartphones of all those involved in the coverup. The former military chief justice herself briefly disappeared and was found after what is suspected to be a staged suicide attempt during which her smartphone also mysteriously disappeared.
It's a strange story; people on the left tend to think she acted for the right reasons but in the wrong way, and ultimately this case is very damaging, both for the credibility of the military justice system, and in allowing the government another opportunity to destroy the credibility of the justice system.
Overall, complicated case but the BBC story doesn't get close to explaining why this case from over a year ago suddenly made headlines during the past week.