How does the store word and load word instructions work?

How does the Store Word(SW) and Load Word(LW) instructions work, MIPS. SW performs the operation MEM [$s + offset] = $t, but in the data-path it looks like they have performed the operation MEM [Data ($s)+ offset] = $t , because instead of taking the value $s as an input into the ALU it took in the data stored in $s.
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