Not remotely true.

Matthew 4:1 devil is the Greek diabolos.

James 2:19 demons is the Greek daimonion.

Matthew 9:35 sickness is the Greek nosos.

Matthew 14:24 wind is the Greek anemos.

However it is true that pneuma means spirit, as in a human being's eternal spirit (or soul) but also the Holy Spirit, and also can mean wind. Indeed, as far as I know, the meaning for wind came first, and is applied symbolically to refer to a person's spirit.

The Hebrew Alma (soul, breath) is similar. In Genesis 1 God creates Adam and breathes into his nostrils the "breath of life." So it's all related.

The claim, as you state it, is simply factually incorrect. Some instances of 'wind' are ἀνεμός, 'illness' is often νοσός, 'demons' often represents δαίμων only 'spirit' is consistently translated from πνεῦμα.

It is true that pneuma can, in various circumstances, mean 'wind' or 'breath'. However the second claim, that it "was considered to be an invisible, fine substance" is an unwarranted extrapolation. It appears to be derived from Stoic philosophy, however there is no overwhelming evidence that Stoic philosophy provided a metaphysical basis for the NT writings. Nor that Stoic ontology was dominant enough for this to be the only understanding. Furthermore, one must continually recognise that the NT documents are written out of a Hellenic-influenced Judaism into the Hellenic eastern Mediterranean, not rather aimed directly into the philosophical milieu of Greek thought.

Some early Christian thinkers and authors, I have Tertullian in mind, adopted the Stoic interpretation of pneuma, but this is a post-NT development.