不思議の国のアリス "yugami no kuni no arisu" is a play on 不思議の国のアリス "fushigi no kuni no arisu" which is the Japanese translation of "Alice in Wonderland". "Yugami no kuni" means something like "Distortedland" instead of "Wonderland".
What is our policy on romanization where a larger phrase includes an obvious western transliteration? I'll use "Alice" for now since it's what's meant, but feel free to change if necessary.
Also it seems Katsuragi Ariko is also called Alice, but since we don't tag nicknames, I'll just go with her real name. That causes less ambiguity problems anyway.
The wiki page says it''s a cellphone game published by Sunsoft.
歪みの国のアリス is a text adventure horror game with multiple endings, following 葛木亜莉子 Ariko Katsuragi, the girl in the illustration you posted.
Here's the synopsis on wiki translated:
葛木亜莉子 Ariko Katsuragi wakes up in the study room after school, to find a man wearing a ash colored robe. The man says he's called Cheshire Cat and calls Ariko 'Alice'. 'Let's run after the white rabbit' With these few words, Alice is led into a distorted world. What truth will be revealed once she has found the white rabbit...?
This article about the release of the game on ipod and ipod touch (before it was available on regular cellphones) says the game spread like wildfire mainly amongst high-school girls.