Italian peers east regularly on walk back from Aldi (8)

'italian peers' is the definition.
I know nothing about this answer so I cannot tell whether it can be defined by this definition.

'east regularly on walk back from aldi' is the wordplay.
'regularly' indicates alternate letters (regularly take one letter, leave next etc.).
'on' means one lot of letters go next to another.
'walk' becomes 'march' (march is a kind of walk).
'back from' says to take the final letters (the letter at the back of the word).
The last letter of 'aldi' is 'i'.
The alternating letters of 'east' are 'es'.
'es' after 'march' is 'marches'.
'marches'+'i'='MARCHESI'

Can you help me to learn more?