As is customary, I read only what you quoted before the article.
The way I understood it is that main incentive was to capture ships, that's on top of the pay; So, like a bonus structure in modern day and age. If you weren't assigned to a ship, you'd still get paid but half of what you'd get on a ship. Since there were eventually more officers than ships, this created a pool of officers eager for assignments and thus "if you won't, there's someone that will" management style.
Now, a bit more complicated what Allen argued about, also from what I understood, is if captains were on fixed wage they'd turn down assignments (which they could since they weren't permanently employed) since reward isn't following the risk and you'd probably get only the worst or desperate captains to accept the job instead of competent which have all the reasons to refuse.
I don't know, maybe I read it wrong, but it makes sense like that at least.