To be more specific,
when browsing to http://www.gigwig.com/ your browser sends this message:
GET / HTTP/1.1
If-Modified-Since: Mon, 05 Jan 2009 21:50:31 GMT
DreamHost uses virtual hosting. What that means is the web server will read the "Host" header value above, and then check a list of virtual hosts (one for each domain or subdomain) in order to process the request.
Thus if you just browse to http://22.214.171.124/ then the "Host" header isn't going to match any virtual hosts and you get a "default" or an error page.
Now obviously if you have added the domain or subdomain as "fully hosted" at DreamHost, you will have a virtual host entry. But usually browsers will need to obtain the IP address from a DNS server. Scott mentioned a trick where you can have your computer skip contacting a DNS server by simply telling it that www.gigwig.com = 126.96.36.199 - this will work while waiting for DNS to propagate, but don't rely on it - DreamHost can change the IP address on you. You can also use the same trick for development on your local machine, just add and remove www.gigwig.com = 127.0.0.1 as necessary.