You can give her one more chance. But that is it.
Don't be suspicious, just have fun together.
Let bygones be bygones.
If you both want to be together, be together.
Be open and communicate about your mutual expectations for the relationship.
Remember though, as far as faithfullness and "cheating" it doesn't really exist in your case. It is all a consturct, or rather a simple mutual understanding between the two of you only. And there is no mine yours ours in the case. You are offered no protections until you are actually legally married. In our society, of course, even when there in a recognized marriage, there are very few legal protections, most especially for the man.
Do you want to marry this girl? If so, in light of recent events, I can understand you wanting to think about it very seriously and take your time. If this insult is not something you think you can ever get over, you may want to think of ending the romance. If so, you don't need to waste anymore of your time. (You don't need to waste any more of hers either, but considering what a busy girl she is, that must reasonably form less of a consideration in the matter at present)
It is true that there are "other fish in the sea" as so many posters and Spanish tv dramas very wisely advise. This is only part of the story however. Yes, by no means, stay with someone only because you can - so as not to have been slighted, or to know you are preffered to the likes of Lenny.
Don't though, let another guy have your goods if you want them. Take them and own them. If she is the person who you prefer above any other, if in otherwords you love her, then you have a right to be happy with her. Just be certain not to be letting little incedents like this happen under your nose again, man up a little, and cut back on the video games.