You likely did not install a program but ran a java applet which is how a lot of chats work.
I have never used this specific site but the chat would not be logged on your computer.
If this concerns you and you want to clean up any records of having used that site do the following.
If you are in any kind of position where you think someone would be using software like that against you then getting rid of the drive itself would be your best move if you wanted to play it safe.
If you did none of the stuff that I mentioned then a good deal could be recovered.