You'd need to clarify what constitutes an "input" in physical cash, but essentially, yes.  You provide the cash register with your money, and in return, they give you change made up of other people's money.  However, Monero operates differently when you make a transaction; your money gets mixed with other people's money, whether you actively choose this or not.

A more fitting comparison with cash would be this:  Every time you spend a dollar bill, you meet 15 strangers.  Together, you all place your dollar bills into a black box without seeing how much each person has put.  Then, you hand this box to the cashier.  She takes out your dollar bill (without being aware of its owner) and divides the remaining money into 15 individual boxes, each belonging to one of the strangers.  Wouldn't that be a mixer? 


I understand his concept of a mixer.  But, generally speaking, a "mixer" can be a wide range of other things.