Origins of the Segment tree data structure
It seems to me that the Segment tree in the Wikipedia article is exactly the same as the segment tree you're used to hear about.

Segment trees as used in programming competitions can be generalized as working over any data type which forms a Semigroup (that is, any data type over which some binary associative operation can be defined on). As a reference, I've been implementing them in Haskell, the source code can be found here.

In this particular case, you'd have to notice that the power set of a set forms a commutative monoid with union, and monoids are, in particular, semigroups. Hence, the particular case described in Wikipedia is a segment tree where the data type is an Interval, and the associative operation is the union operation!.