The only thing I can see that might be a conflict is the difference between 'bool' and 'boolean'.
In Adafruit_LEDBackpack.h (line 376) the function is declared:
void writeDigitNum(uint8_t x, uint8_t num, bool dot = false);
But in Adafruit_LEDBackpack.cpp (line 695) the function is declared:
void Adafruit_7segment::writeDigitNum(uint8_t d, uint8_t num, boolean dot) {
Similarly for writeDigitAscii.
I think 'bool' and 'boolean' are supposed to be the same but I'm not sure how they could end up different, unless someone defines a macro.