Why is xylem a tissue and not an organ?
In plants, there are three types of tissue: meristematic, simple, and complex. 

Meristematic (embryonic and totipotent)

Simple (composed of only one type of cell), such as


parenchyma
collenchyma
sclerenchyma


Complex (composed of more than one type of cell), such as


dermal (protective covering)
vascular (conducting tissue)
xylem (conducts water and dissolved minerals)
phloem (conducts water and dissolved organics)
ground (bulk of the body; primarily parenchyma, collenchyma &amp;
sclerenchyma)


With this information in mind, let's take a look at what the source you provided says that makes up Xylem tissue.


  "[Xylem's] major components include xylem parenchyma, xylem fibers, tracheids, and xylem vessels


Here are the roles of said cells in Xylem:


Xylem parenchyma are cells specific to storage and short distance transport. 
Sclerenchyma Cells (xylem fibers) are specific to support and protection. 
Vessel Members (which are conducting cells) are specific to water, mineral transport, and support mostly in advanced angiosperms. 
Tracheids (which are also conducting cells) are specific to water, mineral transport, and support mostly in gymnosperms and lower angiosperms.


I hope this information helped you understand why Xylem is not an organ, but rather a complex tissue of plant.

References:

http://facweb.furman.edu/~lthompson/bgy34/plantanatomy/plant_cells.htm

http://www.bio.miami.edu/dana/226/226F09_5.html