The Whirling Dervishes are an order of Sufis and Sufism is a sect of Islam.

Therefore, the Whirling Dervishes are both Sufi and Islamic.

Ira Friedlander has written:

'The whirling dervishes, being an account of the Sufi order known as the Mevlevis and its founder the poet and mystic Mevlana Jalalu'ddin Rumi' -- subject(s): Mevleviyeh

'The whirling dervishes'

'Wisdom stories for the planet Earth' -- subject(s): Allegories

Out of the sufi's zidan sufi was the best sufi

No, it is not compulsory for every Muslim. Actually, Whirling Dervish is a sufi kind of dance, practiced in Turkey and its purpose is to feel unity with Allah. This tradition was started in reference with Jalal-ud-Din Rumi, who was one of the major Muslims mystics and is still revered in all over the World, including Turkey.

"Whirling" can be either a verb or an adjective depending on context.

Example:

The rotor started whirling. - Verb

Don't touch the whirling rotor. - Adjective