Not only does a non-Catholic liturgy not fulfill the Sunday obligation, attendance at a non-Catholic liturgy is itself a sin. See Mortalium Animos, para. 8, Pope Pius XI (1928).
If a Catholic cannot attend a licit, valid Liturgy of the Catholic Rite, the obligation is dispensed. Catechism of the Catholic Church, para. 2181. However, he or she is still obligated to keep the Sabbath holy, which could be done by, among other things, praying the Rosary (as choy suggested), reading the Mass for the day at home, watching on television/internet, or some other method. See Catechism of the Catholic Church, para. 2183. One should discuss this with his or her pastor, who has the power to dispense from the obligation and provide a suggested alternate method of keeping the day holy. See Catechism of the Catholic Church, para. 2181.
choy has a good point that goes more toward whether this "law" is a good pastoral choice on the part of the Church, who is obliged to make such laws according to the Church's theology. My guess, from my limited experience amongst the Orthodox, is that many priests in floundering parishes might like the people to feel obligated under pain of "mortal sin" to come to Divine Liturgy. But, the whole idea really doesn't work with the theology and pastoral nature of the Orthodox Church, as choy has adequately pointed out.