I also found this (ironically) abstract. There are more than enough philosophers on this board to translate this for us, but I think it might be useful to give it a shot and let somebody smarter correct the misinterpretations.
The author suggests that the "radical" part of EA is the idea that we are just as obligated to help a child drowning in a faraway pond as in a nearby one:
The morally radical suggestion is that our ability to act so as to produce value anywhere places the same moral demands on us as does our ability to produce value in our immediate practical circumstances
She notes that what she sees as the EA moral view excludes "virtue-oriented" or subjective moral positions, and lists several views (e.g. "Kantian constructivist") that are restricted if one takes what she sees as the EA moral view. She maintains that such views, which (apparently) have a long history at Oxford, have a lot to offer in the way of critique of EA.
Institutional critique
In a nutshell, EA focuses too much on what it can measure, and what it can measure are incrementalist approaches that ignores the "structural, political roots of global misery." The author says that the EA responses to this criticism (that even efforts at systemic change can be evaluated and judged effective) are fair. She says that these responses constitute a claim that the institutional critique is a criticism of how closely EA hews to its tenets, rather than of the tenets themselves. She disagrees with this claim.
Philosophical critique
This critique holds that EAs basically misunderstand what morality is-- that the point of view of the universe is not really possible. The author argues that attempting to take this perspective actively "deprives us of the very resources we need to recognise what matters morally"-- in other words, taking the abstract view eliminates moral information from our reasoning.
The author lists some of the features of the worldview underpinning the philosophical critique. Acting rightly includes:
acting in ways that are reflective of virtues such as benevolence, which aims at the well-being of others
acting, when appropriate, in ways reflective of the broad virtue of justice, which aims at an end—giving people what they are owed—that can conflict with the end of benevolence
She concludes:
In a case in which it is not right to improve others’ well-being, it makes no sense to say that we produce a worse result. To say this would be to pervert our grasp of the matter by importing into it an alien conception of morality ... There is here simply no room for EA-style talk of “most good.”
So in this view there are situations in which morality is more expansive than the improvement of others' well-being, and taking the abstract view eliminates these possibilities.
The philosophical-institutional critique
The author combines the philosophical and institutional critiques. The crux of this view seems to be that large-scale social problems have an ethical valence, and that it's basically impossible to understand or begin to rectify them if you take the abstract (god's eye) view, which eliminates some of this useful information:
Social phenomena are taken to be irreducibly ethical and such that we require particular modes of affective response to see them clearly ... Against this backdrop, EA’s abstract epistemological stance seems to veer toward removing entirely it from the business of social understanding.
This critique maintains that it's the methodological tools of EA ("economic modes of reasoning") that block understanding, and articulates part of the worldview behind this critique:
Underlying this charge is a very particular diagnosis of our social condition. The thought is that the great social malaise of our time is the circumstance, sometimes taken as the mark of neoliberalism, that economic modes of reasoning have overreached so that things once rightly valued in a manner immune to the logic of exchange have been instrumentalised.
In other words, the overreach of economic thinking into moral philosophy is a kind of contamination that blinds EA to important moral concerns.
Conclusion
Finally, the author contends that EA's framework constrains "available moral and political outlooks," and ties this to the lack of diversity within the movement. By excluding more subjective strains of moral theory, EA excludes the individuals who "find in these traditions the things they most need to say." In order for EA to make room for these individuals, it would need to expand its view of morality.