Some Windows programs might run under wine: some will, some won't and games are amongst the things that are least likely to work as games programmers often write as directly as they can to bare metal to speed things up.
The archive manager probably opened because you were trying to do something with a compressed file, which is effectively an archive (with either one file or many files in the archive); if you knew how to use it, it might allow you to de-compress the files, but that's no guarantee they would run.
To install programs that will work, you want the package manager. You should open up, eg, synaptic, tick on the programs that you want and it will grab them and install them for you. Try that with wine and then try some of your existing programs and see if you have any success, but if you can find native Linux programs that do want you want, you'll probably be happier.
- there is more than just synaptic and they may be described as 'add and remove software', but that's a good place to start.
- at some point you will find that you want programs that don't seem to be available; for that you may need to enable extra repositories (stores of programs); search on "adding extra Ubuntu repositories " for more info when you get there