The Abp. says it plainly and at length (around the 35 minute mark): he intends to commune people who have been married in the Greek Orthodox Church who (for whatever or no reason) refuse to actually join the Church, that is, to conscientiously confess Christ in the Orthodox manner. We infer that he means commune those who come to the Chalice.
His answer is logically and grammatically ambiguous. He says that he "personally" disagrees with the Greek Church's stance and that he "personally" would commune the heterodox spouses. It's ambiguous because he is not explicitly and specifically saying that if he knows that someone is a heterodox spouse and if today the person would come to the chalice that he would commune the spouse even when the church has in place rules that ban this. But nor is he explicitly specifying that he is only talking about what he would personally do if he could impose his own beliefs on the church. In other words, he is not specifying whether he would just do this in a purely hypothetical situation absent any church rule, or if in real life when he is put in this situation that this is what he does. He did not explicitly say that he communes heterodox spouses, but nor did he explicitly deny it.
For instance, if you said "Personally, I would join the army", the meaning is logically ambiguous. Someone would need the context to know what you meant for certain. For example, did you mean that you would do it if there were a draft, if there were a war, if you were young or old enough, or all three? Normally, if there was no context, I would interpret this statement to mean that the person would join the army if the situation called for it, ie. if there were a draft, but that by putting it in the hypothetical sense, the statement would mean that currently the person is not going to join the army.
Furthermore, his statement this February was not reported by witnesses as this ambiguous. In what people reported, he said explicitly that heterodox spouses can commune. Supposedly, he did not use hypothetical terms like "Personally, I would do ____."
If it were really important to find out what he said, you could write to the people in the audience and ask for his explicit sentences.
His grammar and the theology it lays out is interesting: he states that we (Greek Orthodox clergy) are separating from one sacrament those whom we have joined with another; that refusing Communion to those married in the Orthodox manner is inconsistent.
I guess that my understanding of the EO theology, if I were going to respond to the Abp.'s explanation, is that the heterodox spouses are allowed marriage by ekonomia. I could be mistaken, but this is my impression. The EO church also allows communion to OOs, RCs, and Anglicans (I don't know about Lutherans) by ekonomia on certain exceptional cases. I guess you could make the argument that being married is an exceptional case that can invoke ekonomia.
One problem with allowing it for heterodox spouses is practical: the EO church requires confession and fasting before communion. Are the heterodox spouses going to do the confession and fasting? Probably not.
The priest seems basically worried that if the heterodox spouses don't get communion, then the whole couple is going to leave because it won't be happy if one spouse can't commune, although he doesn't state it so clearly. I can see that problem, but still, the answer that he proposes doesn't seem to be how the patristic Church works, ie. allowing open communion for the sake of not losing members. There are lots of things that can cause people in modern non-Orthodox countries to leave, not just the issue of communion. Another reason is that GOARCH is seen as culturally very Greek and doesn't do outreach to non-Greeks in the same way that, say, AOCNA has. Theologically, the GOARCH is allowed in fact to give up Greek culture and to do outreach to non-Greeks, but it's not allowed to do open communion.
Another practical objection to his argument is that even if you opened communion, it doesn't mean that people would stay. In the 1950's, the RC Church and the EO church both had closed communion, but the RC Church had a stricter demand of raising the kids Catholic. Certainly in some cases of mixed marriages, RC strictness actually led to kids in mixed EO-RC marriages being raised Catholic and to EOs losing membership to the RCs. So having strictness on issues like communion and raising kids seems possibly to work either way.
To give an analogy, imagine if the Amish are strict and shun anyone who marries non-Amish. They could lose members because some of them will marry non-Amish and won't be welcomed back. But imagine if the Amish loosen up and fully welcome anyone, Amish or not, into all aspects of their communal and religious life, with an Open Door policy. Alot of Amish kids might feel fully open to marry outside the faith, and then in their situation of mixed marriages, they might find that the Amish society is too quaint and doesn't fit their cultural preferences, and that mainstream churches work better, and so they leave anyway. The hypothetical Amish "Open Door" policy ended up with non-Amish acquainting themselves deeply with non-Amish cultural life and finding the latter preferable.
The Amish analogy shows that whether one has a closed door policy or an open door one, a sect can still drain members out. The real reason why they would lose members is not because of an open or closed door policy, but because of other factors, like the fact that they are living in the midst of a non-Amish society, or because Amish ways really are counterproductive (like not using electricity). EOs could be losing members and the closed communion policy could be only a very minor factor in contrast to much stronger factors like failing to do enough outreach to non-Greeks, over-emphasizing Greek culture, being in a society that is becoming less religious or a society that is generally culturally Protestant with some Catholicism.
