It looks like an Exchange but it is not.
For me, that's clearly an exchange. If you get a private key, then you have got coins - that means, you just have exchanged Bitcoin to Monero. These coins are now under your control. While in the exchange process, the exchanger could have stolen your coins, it was clearly an exchange process.
From my point of view, it would be only a mixer if the website presents itself as if the point of the operation was to return to Bitcoin later. For example, if on the landing page you see the heading "Step 1: Exchange to Monero", and then a button is displayed leading you to a "Step 2: Exchange back to Bitcoin". That would be
perhaps the kind of service that theymos described in rule 1d.
I'm not even sure about that, because in theymos' rules there is the following interesting word:
d. If the site internally converts your deposit into other things as part of its mixing
Thus, if you get Monero coins in the process and have control over them, that can't be described as "internally". You are the one who takes the decision to exchange them back.
What you write here:
When you enter their website there is a clickable link for Privacy Enhancement where they provide tips for who wants to use their rights to Privacy. They do not advertise themselves as Mixer or Privacy Enhancement tool but they advise to swap between Bitcoin and Monero regularly to keep up with their Privacy.
... in my opinion isn't enough for the service to be considered a mixer, because it's simply common sense and you could read it as an advice in every Bitcoin blog or forum. The point of the website model you describe, is still to exchange one coin to another.