It's not quite as bad as "a GUI in Visual Basic to track an IP," but it's still a significant inaccuracy. I understand that it can be confusing: Chinese, Simplified, Traditional, Mandarin, Cantonese, Taiwanese -- but it's really quite simple.
The written language is called "Chinese." It uses characters to express meaning, and most of these characters are only vaguely phonetic. There used to be one "official" way of writing Chinese, until 1950s, when the Mainland China introduced the "simplified character set" in an attempt to combat illiteracy and make the characters easier to write. For example, the character for the dragon, "龍" (16 strokes) was simplified to "龙" (5 strokes). These days there are two recognized character sets -- Traditional Chinese, which is still used in Hong Kong and Taiwan, and Simplified Chinese, which is used in Mainland China and in a few other places. To draw parallels to English, writing "gaoler," "cheque," and "jewellery" would be "Traditional English," while "jailer," "check," and "jewelry" would be "Simplified English." (Or, as u can see in teh comments, sum wud say simplified is mor liek dis, but this opinion is likely to be poorly received. :))
Now, on to spoken Chinese. Because, as I said, the characters are only vaguely phonetic, there is a lot of local variation between dialects. People who live in Beijing speak very differently from people who live in Shanghai. People who live in Taiwan speak differently from those who live in Hong Kong. In some cases the differences are dramatic enough to consider them to be two different languages, while in others mild enough to consider them to be merely dialects (and there's no uniform agreement among linguists about this, either). Really, it's just like with English -- Australians, Americans, Brits, and Irish all speak very distinct versions of English. Sometimes the accent can even be heavy enough to be completely incomprehensible (Cockney, or Newfie accents spring to mind). However, if you are from Mississippi and you correspond with someone in Newfoundland, you'll be writing in mutually intelligible English, despite the fact that one will spell it "cheque," and the other "check." You won't be writing in "Southern" (despite probably throwing in a few "y'alls").
What we call "Mandarin" in the West is known in China as "普通话" -- "common speech." Think of it as "the Queen's English" of Mainland China. It's an attempt to make sure that when delegates from Shanghai and delegates from Guangzhou meet in Beijing, that everyone can understand each-other well enough to do some government work. It's pretty much a milder version of "how they speak in Beijing" -- just as "the Queen's English" is a milder version of "how they speak in London." In reality, "Mandarin" makes about as much sense as calling a language "Brit-like." You can sort of claim that Canadians, Australians, and Irish speak "Brit-like," but they themselves would balk at being lumped together, as they are clearly very distinct. Just the same, claiming that people in Shanghai, Guangzhou, and Taiwan all speak "Mandarin" would be inaccurate. In fact, it's pretty much only done for the benefit of cookie-cutter Language courses, where it's common practice to pretend that there's only "Mandarin" and "Cantonese." If you learn "Mandarin" and go to Shanghai, you'd probably not understand a single word of what a street vendor tells you.
So, let's get back to the clip that prompted this diatribe.
So, repeat after me: if it's written, it's Chinese. It can either be "Traditional Chinese" or it can be "Simplified Chinese." If it's spoken, then it's okay to say that someone speaks "Mandarin" (but only insofar as saying that they aren't speaking Cantonese.) Moreover, you can't really say which spoken dialect of Chinese it is by just looking at the writing -- especially not if it's a restaurant sign, and if you're a laowai from Las Vegas (and I say this fully realizing the irony of the fact that I'm a laowai from Montreal.) :)
Oh, and the writing doesn't say "Mr. Hu's Mandarin Kitchen" -- it says "胡先生的喜相逢..." or "Mr. Hu's Happy Encounters..." (Diner? Cafe?). But I was going to let this slide.