The "count the moving blocks" thing will only work on a standard system of blocks. The key issue here is that the black rope does not come back down to the beam. Instead, it feeds into a second system. If you removed that system and simply anchored it in the boom you'd have a 1:1 system.

I find these things easier to look at in terms of rope moved. What does it take to move the boom 1 unit down? Well, if you remove the final block and imagine yourself sitting on the boom, it's pretty obviously 8 units. Now sit back on the boat and use that final block. How much more rope do you have to pull to shift the boom that 1 unit? 1 unit, so you've pulled 9 units, so it's 9:1.

It's not going to be a multiplier because it's not a cascade. There's only one floating block in the system and that's the one that gives you the 2 x 4 = 8 : 1.

Paul