Well, after reading your post, it "jogged" my memory a bit - so a quick google tells me that mepis is based on debian (and/or (k)Ubuntu) which suggests to me that you've not done your homework.
Debian (and most of the derivative distros) are based on the APT package manager, so you're probably wasting your time (at this stage) trying to install an RPM (which conveniently stands for "Redhat Package Manager").
There may (or not as the case could be) be either, some instructions about installing packages, whereby, if the package you're looking for, isn't available from the normal Mepis Sources, instructions on how to add addtitional sources.
I'm using Kubuntu (also debian based), which has 2 graphical installers available, plus the command line installer. If I want extra stuff I can either add another source, and then fire up one of the GUI installers or update the list of available packages at the CLI installer.
You will need to check whats available to you - I'm guessing it's similar to mine, but can't say for certain as I've not tried Mepis.
If it is similar/same, once you have the correct source available in the sources.list (which is what APT looks at to see where it needs to look, to find out what packages are available for it) then either GUI or CLI instruction to install Wine, should also drag in any dependencies