Here, as in general in the definitions of laws, the relevent question is referential transparency, not Eq instances.
(You'll note that generally in the definitions of laws the symbol "=" is used, not "==". Sometimes that's written as "≡", to be even clearer about what it represents, as for instance the
Monad Laws page on the Haskell wiki does.)
For some laws, like the "fmap id = id" Functor law, this is obviously
the only possible interpretation, as both sides of that equation are
necessarily functions, and functions don't have an Eq instance.
So in this case, what the first law is asking for is that "ask >> ask" is the same as "ask", in that any instance of "ask" in a program can be replaced with "ask >> ask", or vice versa, without that changing the program's semantics.