I believe it works like this:

    Initial setup:
    0100 c5 30  lds si,[bx+si]   ; Initialize SI
    0102 04 ad  add al,ad
    0104 e6 61  out 61,al
    0106 eb f9  jmp 0101

    After first jump:
    0101 30 04  xor [si],al      ; Modify color part of text buffer.
    0103 ad     lodsw            ; Read [si] into AX and increment SI by 2.
    0104 e6 61  out 61,al
    0106 eb f9  jmp 0101

So the XOR sort of randomizes memory, LODSW reads that memory back (with wraparound), and then writing to port 61h may or may not play a sound depending on bit 0 of AL.

The part I am not sure about is how SI conveniently ends up pointing at video memory. I thought text memory is at b800:0000, and I am not sure how that's derived from [bx+si]?