I think she was testing you with the game. Asking you personal questions to see what you would divulge and answering questions "truthfully" to see how you would react. Just the comment about thinking about kissing you 10 seconds ago was a test to my mind. And kissing someone else was also a test. I think she wanted to see how you would react.
Was she testing for jealousy, infidelity, resolve, lingering love and affection? Who knows? Maybe all of the above or none of the above.
Maybe she is testing because your detachment is beginning to work. She needs to see if there is still some kind of spark. Keep her hungry! Keep her guessing! Keep her wanting more!
There really just seemed to be a lot of flirting going on in this most recent interaction.
"I walked her to the door and she said sorry if I ruined your night, we will never play that game again. I said I'm good and I appreciated the talk. She said "am I still allowed over tomorrow" and i jokingly said, I'll let you know."
Next time ask her if she wants to play spin the bottle or strip poker. She what kind of reaction you get then!
"And now my mind is wondering if I need to state to her that it is fine if she wants to date or be with someone else as I have no control over what she does but if she sleeps or is intimate with another man than I don't believe I can continue a realtionship with her."
Why would you do that? It is like giving her permission and then adding a nice heaping glob of control with a cherry on top! She is going to do what she is going to do regardless of what you say. Don't give her any ideas,
Me51 W53 S17 S14 M22 T25 Bomb-9/11; A-11/11; I move out 11/11
It's easy to find our bottom, it is our top that requires cultivation.
Every rough spot adds to our emotional constitution. -Barney Fife