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Answer: When Reuven gave money to the airlines via his credit card based on Simon’s request, it is indeed considered as if he lent money to Shimon. This is based on a broad concept known as arvut (guarantorship). By means of arvut, the one who becomes obligated is not the one who received the money (the airline) but the one who requested the money to reach the party he specified (Shimon) (Kiddushin 7a). This concept can be used in creating loan obligations, kiddushin, and transactions. Thus, if Shimon would refuse to pay Reuven back because Reuven did not directly give him anything, we would say "Are you kidding?! When asking Reuven to pay the airlines, you said (or implied) you would pay Shimon back."
Bemare Habazak - Rabbis Questions (654)
Rabbi Daniel Mann
319 - Joining a Shushan Purim Seuda
320 - Receiving Credit Card Benefit on Purchase for Someone Else
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However, the problem is only if the benefit that Reuven receives is, in some way, coming from Shimon (Bava Metzia 69b). This case is different because of the nature of the benefit the credit card company gives Reuven. Because credit card companies benefit when their card is used more times/for larger sums of money, they sometimes give incentives to cardholders to use their card as much as possible. The company, thus, gives benefit to the cardholder, i.e., because Reuven decided to use their credit card; they are certainly not doing it at Shimon’s behest. Therefore, there is no problem of ribbit.
Is Reuven, though, required to give or share the gain with Shimon, and, then, if Shimon waived his rights, would that waiver not be considered ribbit? The gemara (Ketubot 98b) asks about a case in which someone serves as an agent to buy a certain amount of a commodity for a buyer for a certain price, and the seller decides to give more commodity than was requested. The gemara says that if the object does not have a set price, we say that the buyer’s money ended up bringing him more than expected. If, though, there was a set price, we view the extra as a present.
Who receives the present? The gemara accepts the opinion that it is divided equally between the buyer and the agent. Rashi explains that this is because there is a doubt for whom the present was intended. Based on this, the Rama (Choshen Mishpat 183:6) says that if the seller specified that he added on for the agent, the agent keeps the whole surplus. The Rif (Ketubot 57b of his pages) says that even assuming the agent was the intended recipient, the buyer deserves a share because the benefit came through him. The Beit Yosef prefers the Rif’s opinion, and the Shach (183:12) wonders why the Rama wrote according to Rashi as if it is agreed upon.
One might have claimed that our case depends on the machloket of the Rif, Rashi et al., as Reuven got the benefit because of Shimon’s purchase. However, in this case, Shimon is less directly involved with the credit card company than the gemara’s seller is to the buyer. Also, the "present" is part of an ongoing deal between company and client (Reuven), to which Shimon is not a party. The Rashba (Meyuchas L’Ramban 60; see K’tzot Hachoshen 283:7) says that when the present is because of the agent’s relationship with the seller, the agent receives the whole benefit.
In summary, based on your description, Reuven need not credit Shimon for the points benefit, and there is no problem of ribbit.
Kuzari -Rabbi Ari Shvat Kuzari class 8- "Answering Questions on the Kuzari's Proof from Mass Revelation
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Kuzari -Rabbi Ari Shvat Kuzari class 9 - "Seeing is Believing" (parag. 21-30)
These paragraphs elaborate on the theme that seeing and knowing is better than any attempt to prove logically, and begins explaining the difference between Israel and gentiles.
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Kuzari -Rabbi Ari Shvat Kuzari class 8- "Answering Questions on the Kuzari's Proof from Mass Revelation
How do we know that the "claim" of mass revelation to 2,000,000 witnesses at Mt. Sinai is really true? This important class answers all of the questions skeptics ask about this claim of the Kuzari.
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As a preparation for the Kuzari's classic proof of G-d from the mass-revelation at Sinai, we start here with 5 other directions to strengthen our belief which also contribute to what the Kuzari will present as well.
Ein Aya Muscle & Meaning: The Dual Nature of Gevurah (Physical Strength)
Is physical strength and fitness a necessity or an ideal? Although it if often totally overlooked among topics of Judaism, Rav Kook writes that it clearly is also a necessity to deter the many enemies of Israel, but even in Y'mot HaMashiach, in the Messianic era, to a certain extent, it's ideal continues even after our enemies will have been finished off.
