Hi, and welcome to Linux. I'm not sure exactly how Slackware-based distros
work, as I haven't used one before. Judging from the Absolute Linux
webpage, you should be able to use Slackware packages in Absolute. Where you
found all of the other versions (Ubuntu, Debian, Redhat, etc), there should be a
Slackware option somewhere. Click on it, and it should take you to the
available Wine versions, the newest at this time of writing being Wine 1.3.24.
I can't really help you much more with this method, as I don't know how
to install software in Slackware/Absolute
Alternatively, Linux distros generally have a package manager installed (for
example, apt-get/Aptitude in Ubuntu) that handle most of the installation work
for you. I might recommend checking out Absolute Linux's package manager
(sorry, not sure which one its using) and seeing if you can install Wine with
it. This would probably be the easiest method, as long as you don't need
the newest versions of Wine as soon as it comes out (that is, sometimes there is
a delay for the package managers to update their version of Wine).
Hibba.