When I use other browsers such as Firefox or Iron, I'm able to see the IDM download button for video sites such as Youtube but not in Slimjet. The plugin is enabled in Slimjet too.
Try by visiting IDM installed directory in Program files, usually found in “C:\Program Files\Internet Download Manager” then drag-n- drop IDMGCExt.crx extension onto slimjet://extensions page (make sure Developer mode is checked).
Google doesn't allow extensions to download from youtube. If you installed via the webstore I don't think it's going to happen. Maybe a fresh direct install would skirt the problem. You do know that SJ has a native downloader for youtube (but unfortunately, not for other video sites)?
"Please note that all IDM extensions that can be found in Google Store are fake and should not be used. You need to install IDM extension manually from IDM installation folder. Read in step 5 how to do it."