Actually, although your correction (future continuous) is possible, the more usual response would be with present continuous:
Can you come out tonight?No sorry. I'm seeing Hamlet at the National Theatre.
In cases where you already have a plan
(for some future time like tonight), present continuous is typically used.
In cases where you have no plan and make a decision on the spur of the moment, will is typically used:
(Phone rings.) OK, I'll answer it.
For fuller details please see:http://www.englishclub.com/grammar/verbs-m_future.htm