In a word, magic
The Lotus Casino is based on the Isle of the Lotus-Eaters from the Odyssey. As such, its main effect is to render those who stay there in an altered state of consciousness and unwilling to leave:
Nine whole days
I was borne along by rough, deadly winds
on the fish-infested sea. Then on the tenth
our squadron reached the land of the Lotus-eaters,
people who eat the lotus, mellow fruit and flower.
We disembarked on the coast, drew water there
and crewmen snatched a meal by the swift ships.
Once we’d had our fill of food and drink I sent
a detail ahead, two picked men and a third, a runner,
to scout out who might live there—men like us perhaps,
who live on bread? So off they went and soon enough
they mingled among the natives, Lotus-eaters, Lotus-eaters
who had no notion of killing my companions, not at all,
they simply gave them the lotus to taste instead …
Any crewmen who ate the lotus, the honey-sweet fruit,
lost all desire to send a message back, much less return,
their only wish to linger there with the Lotus-eaters,
grazing on lotus, all memory of the journey home
However, the Lotus Casino also has the power to slow or arrest the passage of time (or at least its effects), not merely its perception, to some extent. The person who had been there since the 70s didn’t merely look like he’d just stepped out of the 70s for comedic effect: he had not aged since he entered the building.
“This place is a trap.”
She didn’t respond until I shook her again. “What?”
“Listen. The Underworld. Our quest!”
“Oh, come on, Percy. Just a few more minutes.”
“Annabeth, there are people here from 1977. Kids who have never aged.
You check in, and you stay forever.”
The Lightning Thief
In fact, a major plot point in The Titan’s Curse concerns some demigods who were sent to the Lotus Casino, and who had not aged at all since the 30s.
“Bianca,” I said. “That hotel you stayed at. Was it possibly called
the Lotus Hotel and Casino?” Her eyes widened.
“How could you know that?”
“Oh, great,” I said.
“Wait,” Thalia said.
“What is the Lotus Casino?”
“A couple of years ago,” I said, “Grover,
Annabeth, and I got trapped there. It’s designed so you never want to
leave. We stayed for about an hour. When we came out, five days had
passed. It makes time speed up.”
The Titan’s Curse
This is all rendered a little confusing in the film, since the emphasis appears to be on the lotus-flower snacks (as in the Odyssey), which are missing from the original book. Nonetheless, it is clear that the power of the casino to slow the passage of time is still at work.