"I walk...to the gym" ne peut-il pas être "marcher" au lieu d' aller"

As the lesson notes, in French there is a distinction between marcher and aller à pied. 

There is the general act of walking for which 'marcher' is appropriate - it may be qualified by how, when, why or even 'where' as in a location for walking (je marche dans la forêt), but is not used for the specific act of 'walk(ing) to somewhere'. 

The specific act of using walking as a mode of transport to get somewhere is « aller à pied ». Your example is about « going to somewhere (by foot/by walking) » and « aller à pied » is the best (precise) translation in this case.

Hi John,

What is your question?

It's unclear what it is you need help with?

Jim

Just to complement Maarten's answer: aller à pied always needs a destination. You can't just use it for the act of walking by itself.

You still don't mention any kind of contrast.

You still don't mention any kind of contrast.

You still don't mention any kind of contrast.

Raymond,

my initial answer includes - walking in the …, and walking to (destination). 

The lesson also covers differences. If you give specific situations, I am sure someone in this ‘ community ‘ can/will address them.