The real question is the question of proof. If a person was in a scenario where everyday was an absolutely flawless repetition of Groundhog Day, the question is really one of how many possible solutions are there for such a situation.
As a standard of proof this answer will use Ockham's Razor (please note the spelling of "Ockham" does vary). Namely, establishing what is the minimal explanation for any phenomenon.
One possible explanation is that the recursive world is the result of a simulation. Certainly the person is the only one aware that each is exact repeat and for him it is Groundhog Day every day.
But it is not sole explanation. Also, as an explanation the simulation hypothesis has to make a number of assumptions. (1) The world is a simulation, (2) whoever or whatever is in charge of the simulation has taken the person and allowed them to continue advance through the simulation gaining new memories and experience while everybody else does not or they lose that in the daily reset, and (3) what is the purpose of subjecting only one person to the Groundhog Day recursion.
Actually of those assumptions itself requires their own explanation. In fact, all three explanations are needed to explain the simulation as such.
Simpler explanations for Groundhog Day can be devised. The person is caught in a time-loop type of phenomenon. When he reaches the end of Groundhog Day he is transported back to its beginning. While the nature of the time-loop itself cannot be explained, its consequences conform to those experienced by someone caught in a time-loop. Basically the person experiences the Groundhog Day effect.
The person has become adrift in the multiverse. At the end of each Groundhog day the person is shunted "sideways" and one day "backwards" in time to the beginning again.
The person is a brain in a vat experiencing an exceptionally fidelity virtual reality which is, of course, Groundhog Day. Simulating the world for one person is much more economical hypothesis than the simulation of the whole world.
Voltaire's demon. This concept was a philosophical proposition that reality as we know it was created by a being, possibly a supernatural entity, by manipulating our senses to generate the impression that we were experiencing an actual world. Anyone could be effectively a sort of brain in a vat experiencing an artificial reality from synthetic perception. This means we could be simply conscious spirits floating in formless void with Voltairean demons fooling us into believing we exist in a physical world.
This makes Voltaire's demon the precursor of both the brain in the vat and the universe as a computer simulation.
In conclusion, with the application of Ockham's Razor and the realization that it is possible to construct simpler counter-examples as explanations for a Groundhog Day than the presumption that the existence of a Groundhog Day would be proof for the universe as a simulation. The answer is no. Groundhog Day does not prove the universe is simulation. Because other simpler explanations are also possible. Also, it is not possible to choose conclusively between the alternative explanations. This makes the suggestion of Groundhog Day proves the simulation hypothesis only one possible explanation among many.