The Dalai is NOT the spiritual leader of the Gelug school. The Ganden Tripa is. He was the political leader of Tibet as self appointed since the Fifth Dalai Lama's time until recently when the 14th Dalai Lama retired as the political leader of the CTA. Each of the main schools of Tibetan Buddhism has its own leader. For the Kaygu, the Karmapa, the Sakya, the Sakya Trizin, while there is no official spiritual head for the Nyingma school. The Supreme Head of the Nyingmapa is a position that was established, primarily for administrative purposes, only while in exile in India. In Tibet no one served as the head of this school. First this title was given by H.H. the XIV Dalai Lama to Dudjom Rinpoche. Then it passed on to Dilgo Khyentse Rinpoche, Penor Rinpoche and in 2001, to Minling Trichen Rinpoche. In 2010 Kyabjé Trulshik Rinpoche accepted the position, and in 2012 the title passed to Taklung Tsetrul Rinpoche.
Hence, from the spiritual perspective, Tibet is divided into 4 major schools plus the Jonangs, Bons and minority Christian, Hindu and Muslims.
Mr Johannes's article is very correct otherwise that the Dalai Lama sees the "unity" of the schools of Buddhism as the key to political autonomy. However, the Shugden practice does not favor separation from other schools of Tibetan Buddhism. All schools favor independence practice for reasons of purity of lineage and practice. This being the case, independent practice does not means separation. It can still mean unity under one political head ie the Dalai Lama.