The way that an object reflects light, and therefore how shiny it is, is a function of how much the speed of light changes as it enters the medium (substance). Light travels at different speeds depending on what substance it is traveling through, therefore as light moves through air and then through a piece of glass, its speed will change. Some of the light will be reflected back out into the air and some of the light will be bent as it enters the glass, or refracted.
The measure of how much the speed of light changes as it enters a medium is called the refractive index, denoted n. We measure n by dividing the speed of light in a vacuum over the speed of light through the medium. The speed of light in a vacuum is typically denoted as c (such as in Einstein's famous equation E=mc^2) and is equal to 3 times 10 to the 8th power (3*10^8) in meters per second (around 186,000 miles per second). Therefore the equation for refractive index is n = c / v (where v is the speed of light through the medium or substance).
Using this equation we see that that a vacuum will have an index of refraction of n = c / c ( 3*10^8 m/s / 3*10^8 m/s) which equals 1. Therefore we can use n = 1 as a point of reference; allowing us to compare how different substances will affect light, and therefore how shiny they will be. The more slowly light travels through a medium, the smaller the value of v, the greater the index of refraction and the value of n. Diamonds, which we know are extremely shiny, slow the speed of light significantly and therefore refract light greatly (one of the reasons we value it so much), so we would expect them to have a very high index of refraction, which they do, n = 2.38.
Regular glass, or as I mentioned, soda lime glass, has an index of refraction of n = 1.52. Acrylic glass has an index of refraction of n = 1.49. Hence we can see that light travels slightly faster through acrylic and therefore refracts light less than glass. This is why acrylic is not as shiny as glass.