Testing has shown that Super Mario Run can use up anywhere from 40 to 60 megabytes of data per hour which can add up fast. If you were to play the game for a couple hours a day, it would only take about two weeks to use up 5 gigabytes of data. So, users have to be careful about when and where they play. Of course, Super Mario Run has a controversial policy requiring an internet connection in order to play, which is an anti-piracy measure, but at least for now it can use a lot of data.
It looks like the issue stems from server problems. Nintendo can't quite keep up with the demand for the game, so connections to the game servers are crashing and the reconnects cause the data usage. Theoretically this means Nintendo should be able to fix the problem and the data problems, but at least for now, you may want to make sure you're on WiFi when playing.