What is the official definition of term "adventure travel". How popular
is this type of tourism in the world (especially in europe). What is
the percentage of this type of tourism among other tourism branches?

sorry to be the one to point this out, but there is no "official"
definition, it is an advertising slogan.

Quite true!  But whatever it is, it is popular, especially in Germany,
if I may make a sweeping generalization as an American who lives
there. I have a theory that the Germans (80 million in the area of a
larger Midwast state) want to get away from the crowd and seek
"adventure travel" vacations.  Travel bureaus now offer everything
from bike tours in Mongolia to the Buddhist three-day pilger walk
around Mt. Kailash (up to 5,600 m) in Tibet.
But to your question, alx-ga:  no official definition; popular? What's that?
Popular is going to Mallorca.  If you want a percentage, the terms
need to be defined.

It basically means travel with a twist. That twist is usually a
physical  activity such as hiking, cycling, Kayaking, skiing, etc. But
in recent years, it has morphed to include non-physical activities
such as hot air ballooning, nature walks, boat rides, etc.