Looking at the game files, it looks like this bit hasn't been implemented quite yet. There's a check in the card game for persistent.skip_fights or config.developer to be true, and that enables the "Win the battle" button. However, the skip_fights variable is set to False and never updated.
If you want, this file should allow you to have the skip button, but not enable the config.console or config.developer. Place it in the \games\ folder. Note, it bugs out if you try to skip the tutorial fight, but ignoring the errors seems to be ok.
If you really want the config.console or config.developer, just add those to the file and set them to true.