Mining option seems no more accessible on the site because it might have created lots of negative reviews for freebitco.in they might be trying to do something different but people might actually burn their laptop/pc when trying to get few satoshi from this type of bitcoin mining.
This one seems to be their another failed attempt to look different than another faucet out there.
It's accessible yet, not for everyone as it's an experiment yet for few or some users.
I don't know yet if it worth, maybe for who has powerful machines it can be interesting, but for who has cheap laptops it won't be profitable, it won't pay even the electricity you are spending. Anyway if you want to check when the time comes for all, just set low CPU usage to prevent damage to your laptop.
You're correct that this is just in beta testing and still being rolled out to more users, most certainly not a failed experiment. There is a lot of nonsense being posted about this. You can turn the % CPU used up and down in increments of 10% so there is no reason to overheat anything.
I think you're right about cheap laptops, but with a modern desktop, it looks quite promising. I'm using an old i5 processor at 20% in the background and I've calculated that it's running at about breakeven so if you have something newer and more efficient than that it should be worth doing.
Thanks for warning. Thaught, it would work like the minergate app. Just wanted to try out for fun, not expecting profit results. 
