Do two strongly connected nodes constitute a cycle in directed graph?
Like most things, you should only care about definition if it makes sense and useful in your context.

And in the context of strongly connected component, a nice property we would like to say is that:


  Node $a$ and $b$ belongs to the same cycle if and only if $a$ and $b$ are strongly connected.




This nice statement only holds if you count $f\rightarrow g\rightarrow f$ as a cycle.
So, we would like to count this as a cycle when talking about strongly connected components.