Ofcourse it's real in a sense that it pulls the priv key, shows the pub key and address. But you can do with any program there's nothing special there. The number of pages is so huge that you hardly will find anything manually speaking. Now I don't know if there's a backdoor where the author will see what you search/look for, I cannot speak for this but for extra-safety do not insert your own private key on the site.

There are many sites like this one too, check keys.lol - One guy made an experiment on keys.lol to see if the owner of the site logs/checks the searches whenever someone finds a private key right? This is a fun story, he literally created a new wallet and put in 0.01 bitcoin in it 4 years ago. Then what he did for laughs is "Searched his own private key" inside of the website keys.lol to see which page his wallet is on in that website - this experiment was to see if the owner will empty his wallet or not, then he posted his blockchain public key and told us all to keep an eye open for this one, if the wallet get swept then keys.lol is monitored. To my surprise I still keep checking the wallet, these 0.01 btc are still there.

Which means Keys.lol do not log any searches so if you click "Random" and get lucky with a key nobody else will see it. But I cannot speak of privatekeys.pw myself, I can speak of the other one because I saw the experiment myself.