It's important to play that kind of material slowly at first, as you mention.  It's necessary to get all the details right while you are working through repetitious practice because you are gradually automating it in order to eventually make it second nature when you increase the speed.  

But at a certain point it helps to just go for it and play it faster even though this virtually guarantees a sloppy result at first.  It can be helpful to try playing it faster or up to speed even before you are totally ready because otherwise it's difficult if not impossible to understand what motions are truly necessary when you play that fast as opposed to deliberately playing it slowly.  The tactile feel can be quite different and so it can be a helpful step in the process.

That's not exactly a unique tip, but it is a strategy that can be effective in these kind of situations.  And I'm certain it is more effective than playing the online video game you linked.

Hope that helps.