The news is so sensationalised by using the word "Islamists" too many times in the article.

'The stoning was totally irreligious and illogical,' said her sister, who asked not to be named. 'Islam does not execute a woman for adultery unless four witnesses and the man with whom she committed sex are brought forward publicly.'

This is what is correct and this is what Quran says:

An-Noor [24:4] And those who accuse chaste women, and produce not four witnesses, flog them with eighty stripes, and reject their testimony forever, They indeed are the Fâsiqûn (liars, rebellious, disobedient to Allâh).

The four witnesses have to testify that she committed adultery. If there are less than 4 witnesses and if they accuse the women of adultery the 3 have to be lashed, this is how Chastity of women is protected in Islam.

Al-shabaab are Killers if they did it without following Shariah Law of witnesses and proving the adultery, this case is complicated due to different presentations of the news.