1) There is nothing schismatic about having a private chapel and having a priest perform mass there! It happens all the time.
2) There is nothing schismatic about not being affiliated with a diocese; Opus Dei members, for example, are not, but are in full communion with Rome.
3) It isn't even established in that article that Gibson is not affiliated with a Diocese. Only if the priest who performs mass at Gibson's private chapel is doing so against the wishes of the local bishop would this be the case, and there is NO evidence of this.
4) There is nothing schismatic about celebrating masses in Latin. They do it in Rome all the time, and in many places in the USA. A more important issue is whether the liturgy which is celebrated in Latin is the old Tridentine mass or the new "Novus Ordo" mass, but even the Tridentine mass may be validly and licitly celebrated in the USA with canonical permission.
The article has a great deal of INSINUATION, which you don't have to be a Catholic to detect, just a careful reader. The stuff about Gibson's father and the Latin Mass is totally irrelevant to the question of whether Gibson is in faithful communion with Rome. It is a disgusting smear piece.
I am still awaiting evidence that Gibson worships in any way the Pope would not approve of!
If Gibson adheres to the beliefs of his father, he is a sedevacantist.
Also, there is no evidence that the chapel Gibson built was done under the auspices of the Diocese of Los Angeles. Even private chapels must be consecrated by a bishop in union with Rome. Was that ever done?
The responses on the thread (I should have linked to it the first time) were all over the place. Some Catholics agreed that Gibson is a schismatic while others argued forcefully that he isn't schismatic at all. I don't know who is correct because I'm not a canon lawyer and am not a Catholic.