I've been arguing about the relative merits of various weapon systems with a Chinese military engineer on a War Thunder forum, and the debate has started to get pretty heated. What are some ways I could goad him/her into revealing classified information (as has happened on multiple independent occasions on the forum)?
Goading someone into revealing classified information is a serious breach of security. It may be best to focus on getting the other person to provide open source information that can help you understand their point of view better. Ask them questions about the weapons they favour, such as:

Why they favour them over other systems
What advantages they offer
What drawbacks they have. 

This will help you better understand their point of view, and if you can present a well-reasoned counterargument, it may lead to a productive discussion without needing to resort to trying to get them to reveal classified information.