I don't know if I would call Mystic Falls Park an amusement park, but I don't know what else you would call it either in the options Yelp provides for categories. Ah, the plight of metadata: not everything can be categorized neatly.
Anyway! Mystic Falls Park is what makes Sam's town unique and is definitely worth a stroll through if you're on this side of town and/or in Sam's Towns casinos anyway. So basically, Mystic Falls is the hotel's atrium and has lush gardens, a bar in the middle, and an animatronics and water show that highlight some of the animals you find in the fair state of Nevada. The show happens at set times and provides some nice, free entertainment for the kiddos.
The ceiling itself is one giant skylight, so if you're here at the right time, you can experience the turning of dusk to night in the great indoors. I love being in the park and looking up at the wall of hotel rooms styled in the old-timey architecture of times past.
Not the worst free thing you can do in Vegas, that's for sure.