As far as I can recall, I got into sci-fi and fantasy and military boardgames completely independently from any parental influence. I think it was rare in those days for 'adults' to be interested in sci-fi or fantasy. My father was a WWII veteran, but neither of my parents showed any interest in military subjects.
I was a precocious and voracious reader, and graduated at an early age from the 'junior' section of the library to the adult library.
My father read the occasional history book, and I read every book we had in the house, so that must have contributed to my thirst for history. Similarly, my mother had some interest in mysteries, and I read every Agatha Christie the library had (it was a big library, as I recall). But my volume of reading was much greater than either of my parents, which I can't explain. 
My parents were proud that I was reading a lot, but I don't remember any supervision – they let me read whatever I wanted. I started in sci-fi and fantasy on my own, as well as a lot of books about science and ghost stories and psychic phenomena.
My father played checkers with me until he could no longer win, and stopped. My sister and I played a lot of boardgames with our friends who came over: Monopoly, Sorry! and Life. My parents must have had something against 'military' themed games, as I didn't encounter Risk! or Stratego until I was older.
When I first saw an Avalon Hill game in the store, I was hooked and wanted it, but my father said I was too young. It was not until my college years that I bought my first board wargame (Luftwaffe) and then the first RPGs. Soon I was designing my own games and writing for the wargaming magazines.
My mother was quite surprised that I had such an interest in wargaming, as she said that I was such a peaceful person. She wasn't opposed to it, just surprised.
