You have installed everything correctly, but are missing an ASI loader to actually load vfs.asi. You could for instance use the one that comes with Script Hook or download my trainer and use its ASI loader (version.dll). Then you will be all good!
If the mod manager recognizes that you are in game, that is usually a good sign and indicates that LML has loaded successfully. So you should be very close to having everything running. If you want, you can attach your vfs.log here and I can take a look at what might be missing.