The short tract "The Political Economy of Participatory Economics" seems mostly to have been intended as a 'formal' statement and modelling of Parecon for the academic economist public. The first half of the work restates the case for Parecon in a summary, sort of academic way - for more on this, see Parecon: Life After Capitalism. Then, in response to a challenge by Allen Buchanan that nobody has been able to model an alternative to capitalist market economies yet, Albert & Hahnel create a modelling formula of the principles of Parecon, which they dub the "FMPE" (Formal Modelling of a Participatory Economy). This is highly superfluous on its own, given that it just mathematizes what they have already accessibly described in words, but it is a reflection of the sad state economics as a discipline is in that Albert & Hahnel have no choice but to do this if they want to get through to people in that field. Most important and useful here is the way Albert & Hahnel integrate their endogenous preferences theory, developed in their book Quiet Revolution in Welfare Economics, which will be of interest to heterodox economists.
Along the way, they also address some concerns about the feasibility of their plans, though not any of the more serious objections: their moral hatred of hierarchy leading them to dismiss central planning for no real reason, the degree of bureaucracy involved in their council system which seems to easily surpass that of central planning systems, and the way in which their ideas for consumers' councils greatly seems to exaggerate people's capacity to understand and formulate their own preferences. Then there's the issue that such councils would have to be quite intrusive, as nothing could be bought or sold without councils knowing about it, so that all know about the private life of all in at least that respect. Albert & Hahnel go extremely far in their egalitarianism as well, even proposing to pay more to less competent people who undertake more effort in sports, not just at the top level, but all the way down. But at the same time, they don't seem to have realized that their council system still greatly favors people who are more talented at formulating their preferences and demands over people who are shy, lack self-knowledge, are uncertain about their life-goals, etc.
None of the above objections need defeat the proposal, but I do think Parecon needs an extra round of tinkering or two, with more ideas from more traditional socialist models put in instead of the rather overly egalitarian and optimistic proposal as it stands now. And it's telling that even an absolutely convinced socialist like me would accuse them of those things, precisely the faults socialism in general is often accused of by right-wing philistines; therefore, I may be wrong and underestimating people (as well as Albert & Hahnel), but it's also possible that Parecon as it is now is too much of a good thing.
In any case this booklet is probably not the first one one would want to buy to understand Parecon and the arguments about it, since this is really mostly aimed at economists. The book "Parecon" itself (link above) as well as Moving Forward: Program for a Participatory Economy might be a better buy for that.