I'm not sure why you consider the gauge integral to be easier to understand the Lebesgue integral. It may be due to learning Lebesgue first, but I find it much more intuitive.

Also:

Royden is slightly better in this respect. The first four chapters are excellent, but still probably too theoretical. Further, eventually one will encounter measure spaces that aren't based on the real numbers and the Lebesgue measure,

Yes, this is a good thing. One doesn't understand a structure until one understands which parts of a structure are forcing which properties. Moreover, this supplies useful counterexamples that helps one understand what sort of things one necessarily will need to invoke if one wants certain results.