Yes. The new arrangement of memory implements the logical structure of the linked list.
Here is the code fragment (again):
.data
elmnt01: .word 1
.word elmnt02
elmnt02: .word 2
.word elmnt03
elmnt03: .word 3
.word elmnt04
elmnt04: .word 5
.word elmnt05
elmnt05: .word 7
.word 0
And here is how it is assembled by SPIM:
Each element consists of two words of data: the integer followed by the address of the next node. In this memory dump the nodes follow each other in order.