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Is this an interpersonal utility comparison? If we assume that a rich person will get less utility if he gives 2 dollars away to a poor person?

I am assuming that you mean that the rich person who gives the two dollars would have gotten less utility from it than the poor person to whom he gives it will get.

If so, then this is indeed an interpersonal utility comparison.  It is likely that the rich person will get less utility out of it because of the idea of declining marginal utility.  We are saying that the rich man has so many dollars that each extra dollar he gets is worth less than it is to the poor man.

When we do this, we are comparing the relative amounts of utility that two people get from the money.

No. The situation described in the question is not a pure case of interpersonal utility comparison. Utilities of of same quantity of a good consumed by different person will have different utilities for different persons because of their personal preferences, likes and dislikes. Because of this a small sum of 2 dollars transferred from one person to another person with comparable level of disposable income can have more or less utility after transfer because of the interpersonal differences in their preferences. This question mentions specifically that the 2 dollars are transferred from a rich person to a poor person. Also assumption is made that utility of these 2 dollar is less for the rich person. Therefore this is mare an example of effect of law of diminishing marginal utility. This law states that the marginal utility derived from consumption of an additional unit of a good decreases with the increase in total quantity of that good consumed. The rich person with higher disposable income is able to buy and consume all that the poor person can afford, and still left with lot of disposable income. As the rich person increases his spending, each dollar brings in progressively reducing utility. Thus the utility of last dollar or two spent by rich person is much less than the utility of last dollar or two spent by the poor person.

Krishna, I must disagree with you here.  Let me give you as an example this quote from a paper and I will link below to that paper:

For example, one might
compare Adam’s welfare with Eve’s by counting their daily consumption of apples.
Such a procedure has the advantage of being relatively easy to operationalize, but
it is vulnerable to numerous criticisms. Perhaps Eve is rich and Adam is poor, so
that she can eat as many apples as she chooses but his straitened circumstances
restrict him to only one apple a day. It would then be surprising if Eve did not
derive a great deal less joy from one extra apple per day than Adam

This is exactly the same thing that the questioner is asking with the comparison of the relative utilities that the two people derive from that sum of money.

The paper is entitled "Interpersonal Comparison of Utility" and is authored by a gentleman from the Economics Department at University College, London.

Pohnpei, I did not go through the paper cited by you in detail, but a quick examination of the paper leaves me with the impression that the paper basically deals with methods of comparing interpersonal utilities. It does identify differences in income as one of the cause of such difference, but it does not claim that to be the only cause of interpersonal difference in utilities. The quotation from the paper given by you also only identifies income as one of the cause of interpersonal difference in utilities.

I do not know to with which part of my response above you disagree, but as I see there is nothing in the paper cited by you to contradict my analysis above.