What is a centrosome?
Reading the specified Wikipedia article about Centrosome, actually explains why centrioles are NOT IMPORTANT for the PROGRESSION OF MITOSIS.

To better understand what wiki meant, let us look at both centrioles &amp; centrosomes.

According to Biology Pages for Centrioles and Centrosomes >>


Centrioles are built from a cylindrical array of 9 microtubules, each of which has attached to 2 partial microtubules.
The Centrosome


is located in the cytoplasm usually close to the nucleus. 
It consists of two centrioles — oriented at right angles to each
other — embedded in a mass of amorphous material containing more than
100 different proteins. 
It is duplicated during S phase of the cell    cycle.  
Just before    mitosis, the two centrosomes move apart until    they
are on opposite    sides of the nucleus.  
As mitosis proceeds,       microtubules grow out    from each
centrosome with their plus ends       growing toward the    metaphase
plate. These clusters of microtubules    are called spindle
fibers.



So, now we know that during mitosis, the nuclear membrane separates and the centrosome nucleated microtubules (parts of the cytoskeleton) can associate with the chromosomes to fabricate the mitotic spindle.

Understanding the conceptual working of centrosome, the Wikipedia article states >>


  Interestingly, centrioles are not required for the progression of
  mitosis.
  
  When the centrioles are irradiated by a laser, mitosis
  proceeds normally with a morphologically normal spindle.
  
  In the absence of the centrioles, the microtubules of the spindle are
  focused by motors allowing the formation of a bipolar spindle. Many
  cells can completely undergo interphase without centrioles.


Therefore, even in the absence of centriole, centrosomes develop Astral microtubules which just exist amid and quickly before mitosis. Astral microtubules are characterized as any microtubule beginning from the centrosome which does not interface with a kinetochore.

Astral microtubules are not required for the movement of mitosis, but rather they are required to guarantee the devotion of the procedure. The capacity of astral microtubules can be by and large considered as assurance of cell geometry. They are totally required for right situating and introduction of the mitotic spindle assembly, and are in this way required in deciding the cell division site in light of the geometry and extremity of the cells.

An important note from the the Wikipedia article >>


  Unlike centrioles, centrosomes are required for survival of the
  organism. Acentrosomal cells (i.e. cells without centrosomes) lack
  radial arrays of astral microtubules.
  
  They are also defective in spindle positioning and in ability to
  establish a central localization site in cytokinesis.