this question (two parts) came up.
saw in Seforim that a card game which normally involves writing should not be played on Shabbos due to fear of coming to write
1-is this limited to writing, what if person usually uses a electronic device to keep score?
2- they were playing on Shabbos and keeping score by using a book mark in a book.
struck me as being off but had no hard proof.
The Chayai Adam (quoted in Shemmiras Shabbos Kehilchaso 16:32) prohibits playing games that usually entail writing because of the concern that playing these games will lead to writing. The same would apply to a game that is usually played using an electronic device, like in the case of your question.
All the best
Heard from HaRav Gans shlita.