According to FinCen's website:
The term "money services business" includes any person doing business,
whether or not on a regular basis or as an organized business concern,
in one or more of the following capacities:
(1) Currency dealer or exchanger. (2) Check casher. (3) Issuer of
traveler's checks, money orders or stored value. (4) Seller or
redeemer of traveler's checks, money orders or stored value. (5)
Money transmitter. (6) U.S. Postal Service.
An activity threshold of greater than $1,000 per person per day in one
or more transactions applies to the definitions of: currency dealer or
exchanger; check casher; issuer of traveler's checks, money orders or
stored value; and seller or redeemer of travelers' checks, money
orders or stored value. The threshold applies separately to each
activity -- if the threshold is not met for the specific activity, the
person engaged in that activity is not an MSB on the basis of that
activity.
No activity threshold applies to the definition of money transmitter.
Thus, a person who engages as a business in the transfer of funds is
an MSB as a money transmitter, regardless of the amount of money
transmission activity.
Notwithstanding the previous discussion, the term "money services
business" does not include:
A bank, as that term is defined in 31 CFR 1010.100(d) (formerly 31 CFR
103.11(c)), or A person registered with, and regulated or examined by, the Securities and Exchange Commission or the Commodity Futures
Trading Commission. For the complete regulatory definition of "money
services business", see 31 CFR 1010.100(ff) (formerly 31 CFR
103.11(uu)).
Note: Each money services business (MSB) is a financial institution.
For the regulatory definition of "financial institution," see 31 CFR
1010.100(t) (formerly 31 CFR 103.11(n)).
Based upon this definition, the business described in a money services business because it sells stored value in an amount of $1,000 or more per seller per day.
This business must be licensed as an MSB to do business with customers in the U.S. and is not a legal business model. It probably meets the legal definition of criminal money laundering. The source of the gift cards is also an MSB and a participant in criminal money laundering.
MSBs are required to have an appropriate anti-money laundering program in place and to know, at least, the identity of their customers although not to the same level of detail as securities brokers. Dealing with anonymous customers with "zero KYC" in the context of this business model is not legal. See generally the FinCen guide for MSBs.
While this question has primarily evaluated the legality of the business from a U.S. law perspective, it would constitute illegal money laundering under the laws of most countries, not just the U.S.
