I see what appears to be Rick Warren in the picture there. I heard a preacher lambast Rick Warren for joining 'Chrislam' but read the website and it was about a group of people having a 'dialogue.' I didn't find any major thing over which to condemn Rick Warren, personally.
I haven't watched the whole video-- man, over 40 minutes? Couldn't someone link to a one-page article.
I am all for presenting the truth in Bible translations. I am not sold on one manuscript tradition or the other. I don't think people who read the NIV are all going to Hell. I've known a number of Wycliffe people, though, and it does seem like some of them have lose ideas about translating-- translating from the NIV for example, into the target language, using other study tools. They are trying to get the word out there, but sometimes it sounds like they aren't that rigorous. But they also have some very well studied people in Linguistics and languages. People have different qualifications. It's tough, though, if you've got just a few people in the outside world who can translate the Bible into the target language. They don't know Greek and Hebrew, and they just use what tools they have.
As far as translations that are 'friendly' to Muslims, there may be some truth to that idea. I know of some people doing church planting in their home countries that like to use language familiar and friendly to Muslims. For example, using Ibrahim insead of some other pronunciation of Abraham that was filtered through a few different languages. I'm a little uncertain about 'Isa for Yeshua, though, since that also means Esau. I've read there was another Arabic way of saying it that is supposed to be more authentic to the Hebrew. That's an incredibly important name. I'm thinking of just using "Yeshua" if I'm in that situation. But I'm find with Arabic-derived pronunciations of other names, which are often more similar to the Hebrew than English names of Biblical characters.
As far as I know from what I've read, it is likely that Allah is cognate with the Hebrew word Eloah, but with a definite article thrown on and contracted. Allah is believed to be a contracted form of Al illah. Illah is congnate with Eloah. Elohim is the plural of Hebrew Eloah. From what I've read, what meager evidence there is seems to indicate that Christians might have called God "Allah" in Arabic before Muhammad, but evidence is scant indeed (names of Christians.) The word may have also been used for a moon deity. But Canaanites used the word "el" to refer to false deities, even as the personal name of a deity that did not resemble our Creator, the head of the pagan pantheon in an early stage of Canaanite religion.
There are millions of Christians who don't use especially Islamic language whose Bibles use "Allah" for God. Arabs, Maltese, Indonesians, and maybe some others.
I don't know if their translations leave out 'Father' and 'Son.' I did have a conversation with an Arabic-speaker who was a fairly new convert, but interested in a very contextual approach to presenting the faith. He said the Muhammadan confession that Allah has no son. He said the word for son is a very biological term, so he suggested translated the word son with a different word 'walad.'