When you drag the line gets longer based on how long you drag. This has an influence on your jump strength. Thinking about it do you use an hdpi monitor? Could be that this is broken with high resolutions.
If you want to replay it for the gameplay that is what timed mode is made fo. And in theory the game should save that you read the initial dialogue (or did you use the reset progress button?). But yes in generall skipping dialogues is a thing that I will propably add in a postjam version.