Okay, to respond to this, we need to go a bit more in depth. I apologize this will be long, I simply wish to be absolutely thorough.
A TL;DR is this: It isn't exactly about their intents, it is about the author's data. The authors did not intend to make a claim about oligarchy, so they did not gather data detailed enough to make claims about oligarchy. Their data is only populated enough for them to make definitive claims about the upper 10-20% of people (approx. 35,000,000-70,000,000 people). If you wanted to, instead of adapting the data, just change the definitions, you could, but it would be far from main stream acceptance, as most reasonable people would not consider 35 million to 70 million people a "small group" in the United States sufficiently small to be an oligarchy.
When it comes to a number of the hard sciences, you don't have the problem of operationalization as much as in the soft sciences. When one has a concept of what it is that they want to measure, they need to define it, and then operationalize it into something that they can use to measure and represent it. The more accurate the operationalization of the thing, the better the data will fit the theoretical model being proposed.
Within theory, the author can make up just about anything they want. Any reader can make up anything they want. You can say democracy is a centralization of power in the hands of a single individual, even if most other people would define that as autocracy. You could, because you're the author. And then, when you operationalize and attempt to measure centralization of power in the hands of a single individual, you'd then say your data is supporting the theoretical model that is presented in the paper. You are free to redefine what that author says is democracy, and say "No, that author is really talking about autocracy, he or she is just using a confusing word for who knows why."
What doesn't change however is what the theoretical concept defined by the author is operationalized into. The data that is collected remains rigid across different theoretical models. When one creates the new theory and defines the concepts, they can say that instead of calling it democracy, they call it autocracy to be more in line with what most people mean... but the data remains the same.
The data does not change when theory changes, nor conceptual definitions. All that changes is the application of that data.
So, lets go into a hypothetical. Say we wanted to support the claim that there is oligarchy in the United States. We ask ourselves "Is the United States an oligarchy?", research question! We first need to define oligarchy before we can theorize and then hypothesize. We could say it means 25% of all power in the United States is held in the upper .1% of the income bracket. That's our definition. So we have to go out, and gather data on whatever we operationalize power to be, and be able to root it on a per sample unit basis with income bracket level. If we want to avoid weighting, we will need an insane sample size for us to draw conclusions about each percentile, so instead we aim for a representative sample of the upper .1%, the upper 1%, 10%, and then 50%. We gather the data from samples at each of those ranges. We say that we find support that by how we operationalized power, that the upper .1% has 27% of the overall power in the United States. So we supported our hypothesis, which backs our theory. Yaaaaaaaaay!
And then some asshole comes along who writes "I disagree. It isn't an oligarchy until 50% of the power is in the upper .1% because X, Y, Z." Well, just because this person claims it, the data doesn't change. But now under their theory, the United States is not an oligarchy, because of how he defined his terms. The data is constant, the term has changed.
Now, back to this paper and the topic at hand. Everyone here is free to define oligarchy as they see fit. They are free to do so, using the word as another variable to represent a concept. But just because they use it as that, doesn't mean everyone else will agree with that. You can call an orange an apple, but most people will just raise an eyebrow at you and say "No, that's an orange.". Well, the same is true with oligarchy. You can finagle the term around, but generally it refers to a small group of people with a vastly disproportionate amount of power over policy as opposed to everyone else.
Lets say you wanted to do, as you are suggesting, to take Gilens and Page and draw a conclusion on oligarchy. You would either:
1- Have to redefine oligarchy to a disproportionate amount of power resting in the upper 10-20% of people.
Or 2- Use their data to test a hypothesis about the upper .1% of people and their power.
If you do the first, go ahead. But you'll have to reevaluate on a case by case basis probably close to every other piece of political science literature that is grounded in oligarchy, as most political scientists use oligarchy in reference to a small group. 10-20% of people is far from a small group, and most people should agree with that when we're talking 1 in 10 of 350,000,000. 35,000,000 to 70,000,000 isn't a small group of people.
If you want to do the 2nd, that's where things get tricky. As we know, the data has not changed. Their data is not detailed enough to make calls about the .1% of people, and their level of power. Their data is only accurate enough to give them determinations about the 50% income bracket voters, and upper 10-20% income bracket voters. They don't have nearly enough samples of .1% income people to make any claim about how much power that upper .1% has, only about the upper 20%.
So, you could take their data and run with it to draw different conclusions, but the conclusion of oligarchy can't really be drawn from their data: they don't have detailed enough data for that, and data doesn't just change when someone's definitions do or when they try to take it another way. It isn't about the intent of the authors to support or not support this argument, it is that they didn't gather data to test oligarchy in the first place, understanding oligarchy as the upper .1%. They only had data detailed enough to make determinations about the upper 10-20% of people, which as I argued above, 35m to 70m people is far from a small enough group to be considered an oligarchy to most.
Take that for what you will. I don't honestly think you can run away with the definitions and still be seen as doing anything other than being contrary for the sake of being contrary, nor can you adapt their limited data to such a small group of people.