This is a bit of a mystery. The "England" and "Scotland" teams played several games in 1881 (see http://www.donmouth.co.uk/womens_football/1881.html for details) but all other games were, from reports, clearly played to Association Football rules. However, a report on one game in the Liverpool Mercury of 27th June 1881 suggests that - for this game at least - the players may have been playing a version of rugby.
Note that points were not introduced into rugby until 1886. Until then rugby games were decided by "goals", which could be scored in open play (a "field goal", which was not abolished until 1905) or from a free kick - or "try" - at goal awarded after a touchdown behind their opponents' line. Only if goals were equal were the number of tries counted.
The description of this game does, taken in isolation, sound more like rugby than association football if it were not for the fact that the same teams tended to play "soccer" in their other games. Unfortunately after over 130 years it is impossible to know what they really were playing that afternoon.
cigarette cards and other depictions of women "rugby players" from the period.