You're asking if a girl can loose her virginity through playing sports or games.
Not quite. What you really mean is "Can she tear her hymen through vigorous physical activity, as in sports games or horseback riding?" Yes, and many women/girls do experience this. Does it mean she is no longer a virgin? No.
Virginity is defined as not having experienced sexual intercourse (or penetration to ANY degree) with a penis. That leaves room for a lot of other behaviors that might make parents or on-lookers wince... but without penetration, technically, she remains a virgin.
A lot of cultures place a great deal of significance on the un-torn hymen. Most western cultures no longer put as much emphasis on it nowadays, but some do.
As for an "internal virginity"... that's a concept that has not be defined. Other than the hymen, there's no other "seal of pristene condition" that exists.
It would be unfair to try to judge a woman by the state of her hymen in today's modern world. Use of tampons, horseback riding, and liberal morals all mean that a woman may no longer have an intact hymen OR virginity by the time you get to her. So what? Relax and build trust and a relationship with her. That's more imporant that an outdated concept of purity.