What does "the exercise of vital powers along lines of excellence in a life affording them scope" mean?

Happiness is the exercise of vital powers, along lines of excellence, in a life affording them scope.

This is a precisely-worded and carefully chosen sentence! So it is impossible to put its precise meaning into other words. Bu this is somewhat close:

"Happiness" is the condition whereby a person can and does perform the most important functions of their life, is very successful in doing so in an objectively "good" way, and is fortunate enough to not be prevented from doing so by the circumstances of their life.

Your vital powers are whatever strengths or abilities you have.
To be happy you must exercise them = put them to use.

The phrase along lines of excellence has the vagueness of the finest platitudes, but we can take it as meaning that it's no good to exercise your powers randomly; you must seek the best uses for them.

Finally, all your powers and diligence will do you little good if your circumstances are too constraining; you must have scope, an open field of possibilities, in which to work.

I break the sentence down into three parts: (the exercise of vital powers) (along lines of excellence) (in a life affording them scope)

The first is fairly easy. For short, it could be changed to "active living" or "living with intent".

The second part is simply that exerciser of vital powers from part one ought to intend to improve the way they live according to some standard of quality.

The hardest part of the sentence for me is third part, especially "scope". In my experience of English, it is usually qualified as "scope for [something]", like "scope for action" or "scope for display".

Here, he uses it to mean (I think) the area bounded by external limits of a person's life. A person who was blind all of their life would, in Aristotle's view, not be sad they did not learn the purely visual arts.

So, in the second person, it would be something like "consciously trying to improve yourself where ever you can find room for improvement".

vital powers = your energies

along lines of excellence = performing with excellence

in a life affording them scope = in a life where they have both the freedom to act and opportunities to act on significant matters