I just got this domain from my friend so I need your opinions about value of this domain. It was famous in 2009 and it still kept good alexa rankings (6 mil.)
I didn't get your point when you said that it was famous in 2009. What was famous in 2009? It is a domain name, domain names are not famous without websites. It is a domain appraisal section and your domain does not have a website (at least not right now). It is redirected to some other website and alexa of 6 Mil is nowhere near to good. Dating twitter can not be worth a lot unless it has some application/website attached to it. Moreover twitterdating would have been more meaningful.
The fact it contains Twitter in the domain name would deter me. Twitter went after TwitterSearch.com (not even a "typo domain"), so I don't see why it wouldn't get this one if it ended up on their radar (and isn't already). So, it's a risk. No value, other than as a headache.