The origin of chess seems to lie in an Indian game in which all four branches of the military (infantry, cavalry, elephants, chariots) were represented. While I imagine that elephants can do things which horses cannot, why keep chariots when cavalry is available? Were they not abandoned throughout the world because they were inferior? Consider that they are less mobile and prone to break and the overall fighting power of horses is reduced if one man focuses alone on guiding them while every man is a fighter and a rider at the same time in cavalry. So what are the advantages of chariots?
I am a bit confused about your question, whether you're asking about chess or the value of chariots or if you're trying to compare them to mounted riders. Perhaps if you could clarify your question you may get better answers.
I'd like to offer a comment on your chariot versus mounted rider comparison though. Chariots were used as a stable platform for archers. A mounted rider is useless with a bow unless you also give him stirrups to support his weight off the saddle. But stirrups are a relatively late invention.
The oldest example of a stirrup-like device is from India around the 2nd century BC, a kind of loop in which the rider could hook the big toe of each foot. You can see this in sculptures at Sanchi or Mathura from the period. From India, the idea was transmitted via Buddhist missionaries to China, where they adapted it to a whole-foot stirrup. The earliest examples of this are from Hunan around the 5th century AD. Between the 6th - 8th centuries, the stirrup spread to Central Asia and then on to Europe.
So chariots were definitely more useful than mounted riders as platforms for archery until the spread of the stirrup. Chariots also protected the archer, they could be used to intimidate or trample foot soldiers, and sometimes had blades or scythes attached to clear a path through the enemy. The downside, of course, is that they required flat ground and could be bogged down and made useless in mud. And they were prone to breakage.
My understanding is that chess originated in India during the Gupta Empire, around the 3rd-5th century AD. Stirrups may not have been so widespread then, and consequently there was a greater reliance on chariots. At any rate, I don't think it's fair to draw conclusions about warfare from a game. All we can really say is that chariots were not obsolete at the time.
The history of the stirrup I related above is from the book Medieval Technology and Social Change by Lynn White (Oxford University Press), specifically the chapter "The Origin and Diffusion of the Stirrup".