A review of his Mandarin based on a close listen of the first 5 minutes of the video and listening to the rest in the background while I type this (let me know if it changes later):
tl;dr - Definitely ILR 1+, probably an ILR 2. Pronunciation needs a ton of work, but that's not the only aspect that is measured when analyzing speech. The foreign policy article (linked in another comment) is overly critical, imho.
Detailed:
ILR LEVEL
He's definitely at least an ILR 1+. He shows signs of ILR 2 characteristics (and is probably an ILR 2), but it's hard to tell if he can sustain them in a wide range of contexts. While his pronunciation needs A LOT of work, the language itself is comprehensible to a sympathetic native listener. I strongly disagree with the Foreign Policy article that says it was "terrible". I would say that it's actually kind of amazing given that he's the CEO of a huge company. I would roughly say that he is on par with a good / above average 3rd year student at a school with a really good Chinese program. The original article says 2nd year, but this would be a superstar 2nd year student who was either a heritage speaker or had spent a lot of time in China (e.g., as a homestay or study abroad).
DISCOURSE STRUCTURE AND STYLE
He is able to sustain the dialogue for a long time. He is able to circumlocute decently (this really opens up the ability to communicate), but I would really like to see his range of circumlocution. He is able to string together his sentences in moderately cohesive paragraphs. He does not demonstrate the ability to combine paragraphs cohesively at a high level (signs of an ILR 3), but I don't think the tasks really required it.
His style of answering questions was very American -- very direct. I don't think that a Chinese speaker who has lived exclusively in China (i.e., not educated or trained in the "West") would answer the same questions similarly. In this case, I actually think that it's best for him to answer in an American way even if he could answer in a Chinese style, but that's a different and longer discussion.
Early on when he tells the story of his wife and her grandmother, he really comes across as quite charming.
GRAMMAR
He does decently enough. There are errors, but it's not hard to understand what he is saying -- especially for a sympathetic native listener. The sample didn't really demonstrate a wide range of grammar, but the tasks didn't necessarily require a wide range. He is able to say complex sentences (i.e., two independent clauses), and he is able to speak in different timeframes (normally tenses, but Chinese tenses are not like English). This all points to a solid ILR 2, but grammar is definitely not the toughest part of Mandarin.
VOCABULARY
He has a decent vocabulary -- it's solid for the task. I wonder what his vocabulary is like outside of the topics of personal bio information, Facebook, and Facebook business. If he wants to get to ILR 2+ or ILR 3, he will need to work on the accuracy and diversity of his vocabulary.
PRONUNCIATION
This is easily his weakest point. He has a HEAVY American accent. He mispronounces a lot of words. His tones are WAY off. He seems completely unable to say English loan words in Chinese (e.g., Facebook, Google, etc.). It's actually kind of hard to listen to. That being said, I would say that it is all comprehensible to a sympathetic native listener.
SUMMARY
Overall, really good for someone who is not studying full time and has a very involved full time job. I wonder how much of it was practiced or rehearsed -- a lot of the questions are ones that he definitely _should_ practice (e.g., the story about why he started studying Chinese), since they are standard questions that would be asked to him and/or the Facebook CEO. Regardless, speaking in a foreign language to a large group of people is not easy, and he came across really well.
RECOMMENDATIONS
He can work on his pronunciation in several ways:
- Listen more. Even if it's on in the background, it will help. Right now, I don't think he has a good intuitive sense when he is mispronouncing a word.
- When working with a teacher, do lower level language tasks, and act like a native speaker whose voice/accent he likes. Research suggests that this lowers affective filters for pronunciation.
- Work with suprasegmentals with a pronunciation program that visualize what he's saying. It can be enlightening.
- Practice over pronouncing words. If he does what he perceives as a "caricature" of pronouncing the word, he will probably be closer to accurate.
Other than that, listen more, read more, and I think he will become a rock-solid ILR 2 with room for growth if he wants it.
That's my quick-and-dirty. I am very interested in the informed opinions of others.