I just ran "Check For Updates" and it told me I was up to date and I'm on 5.1.0.914.

So something is not working there.

I get same.

Sometimes companies release minor updates that are reflected for fresh downloads but don't have the auto-update mechanisms in existing clients to download the update --- usually to save on bandwidth costs.

However, for a security patch that seems 'unfortunate'.

Skype's blog post specifically says you can update from the client.