Swiss German is considered a dialect even though I could initially understand Dutch better than Swiss German. I studied 6 years of German, studied in Germany, and grew up with a German speaking grandmother and I still understood nearly nothing. Perhaps what hinders Swiss German from language status is that the dialects differ greatly. In Zürich, I is "ich" with the "ch" coming mostly from the throat. In extreme Western dialects, like Basel, the "ch" is not as exaggerated as in Zürich. In the Eastern dialects, like Sanktgaller Dialekt and Appenzeller Dialekt, the "ch" retains it's power except there are changes such as "ich bin" being "i bi." (younger people from the West sometimes speak like this too)
Another comical example of how unstandardized Swiss German is, is that "oben" (above) is "uni" in Appenzell Innerrhoden, "ufe" in Appenzell Ausserrhoden, and "ue" in the rest of the country with the exception of Wallis I believe. (Wallis dialect is the most unique in all of Switzerland) There are 3 words for above within 15 kilometers of another.
One thing that really distances Swiss German from High German though is the past tense of "be." There is no "ich war" in Swiss German but rather "i bi gsee" or "ich bin gewesen" in High German. When you hear "gsee" it's a tell tale sign that you're listening to an Allemanic dialect.
So, long story short. Swiss German is a dialect but I believe the differences between Swiss German and German are much bigger than say Spanish and Italian. If you are interested in Learning Patrick, learn a very neautral dialect and you can find that you can easily understand other dialects like Swabian and even though Austro-Bavarian dialects to a small extent. My New Year's resolution is to start speaking Swiss German actually