You won’t be able to use DreamHost redirection, or other “hosting” services without a hosting account.
What you can do is set the nameservers for your DreamHost registered domain to a nameserver where you do control the hosting, and establish any DNS records there necessary to “redirect” (I’m not sure how you are using the term here) the lookup to the other site.
The tools other services offer are often not “one-for-one” comparisons even though they use the term “redirect” (many are just framed display of other sites, etc.).
The bottom line is that customized DNS records on DreamHost are only available with hosting plans, but you can point the DreamHost registered domain to other nameservers so, absent a DreamHost hosting plan, that’s the way you will need to go.
edit: While your question is somewhat similar in nature, this thread is over a year old, and your post would probably have been better placed as a new thread.