The employer is paying half of the social security on behalf of the employee. i.e. if the employer did not have to pay FICA they could pay the employee that amount instead, with no increase in their total compensation for the employee. It was an attempt to make the bit on the employee not look as large as it is.
I do not like that FICA and Medicare are referred to as payroll taxes.
I agree, Years ago I worked in NYC and payroll taxes were defined as all the taxes taken out of your paycheck.
FICA - Fed Tax - Medicare - State Tax - City of New York Tax
All of those were called payroll taxes