Why is condensation in dyed beverages colorless?
Given that the majority of beverages such as Gatorade is water, as stated in the comments, the condensate is predominantly water, as can be seen in the Patent Electrolyte blends providing reduced salty taste (which includes Gatorade), that water amounts to well over 99% by composition, of course this will vary. The dyes themselves don't make up much of the volume.  

A common food dye used, according to the Indiana University online experiment webpage How Much Red Dye is in My Gatorade®? , is the red dye, also known as 'Allura Red'

its properties according to the Wikipedia page are stated as:


  It usually comes as a sodium salt, but can also be used as both calcium and potassium salts. It is soluble in water; Its melting point is above 300 °C (572 °F).


It is likely that the majority of the food dye based salts would remain in solution.

Any salts (such as the example above), transported with the evaporating/condensing water would be too small of a concentration to cause any visible effects.

A similar question and answer is Does salt vaporise?