the version you saw in theater WAS the original DVD release. The other version initially released on DVD under the name "director's cut" was indeed shorter than the theatrical version, but Oliver Stone wanted to make the pace tighter and more consistent.
On second thoughts (third thoughts?), he eventually decided to unleash the full story in the Final Cut which adds 40-odds minutes to the film.
There were three separate releases of Alexander on DVD. The first two were released after the theatrical release. There was a 2-disc Widescreen original version of the film from the theater with a white cover. There was also a 1-disc Fullframe Director's cut which cut about 8 minutes of footage and also a 2-disc Widescreen Director's cut I believe containing the same content as each other. The Final Cut was the latest release and contains 40+ minutes of added footage and heavy re-editing. An awful lot of releases for one movie. Hope that helps.