I'm looking to create a Twitter map visualization much like these:
http://beta.twittervision.com/
However, according to the Streaming API docs:
https://twitterapi.pbworks.com/Streaming-API-Documentation#locations
Twitter only permits streaming API access of an area's bounding box with each side's length equal to only one degree of lon/lat.
How are these sites executing these queries despite Twitter's limitations? Is there something I'm missing?
They are most likely using the statuses/sample url, as it just gives them random tweets. As long as the post comes through with location data, they can use it.
As long as the tweets that are being sent come with Lat/Long data, they would be able to plot them on the map.
Note that you can apply for elevated access levels on the streaming API. Elevated level give you more bounding boxes to work with, and allow you to specify more bounding boxes in the query string.
Looking at the two applications you mentioned, they are definitely not displaying the full stream of geolocated tweets. They may be combining the sample or filter stream and either taking only geotagged tweets, or doing geo lookup based on the location field, or a combination of the two.