WK's descriptions of the Shadow flashbacks had me thinking about his dog's age. In one of the flashbacks he arrives at Thamasa and meets Interceptor. He then spends enough time there to get to know and impregnate Relm's mother, and leave. I'd say that could be anywhere from 6 months to a year. Relm is 10 when she joins the party. So add in 9 months for pregnancy and that means the game takes place anywhere from 11-12 years after Shadow first arrives at Thamasa. Assuming Interceptor is only 1-2 years old when he meets Shadow, that makes him about 12-14 years old during the game. A pretty old dog to be travelling the world and hurling himself at monsters!

So here's my crackpot theory...Interceptor is an esper guarding the town of Thamasa. Either that or he has magical properties much like the city's residents.