The algorithm actually does make sense for positional systems (or compact notations in general). Think of long multiplication: it assumes you can multiply by a one-digit number, and lets you get from there to multiplying by a many-digit number. This is the same thing, but it only assumes you can multiply by two, instead of by any one-digit number. So this is a variant of long multiplication, and equivalent to performing long multiplication in binary. But it only makes sense if you have a compact representation of your numbers, since otherwise you may indeed just perform the multiplication directly by counting out 7 stones for the first goat, 7 for the next, and so on.

It is the version described by Lienhard - which involves counting out the whole number anyway, which you could just as easily do without any special algorithm - that is pointless.