What difference does it make if work is just a little bit fun? Logically, fun is a distraction and there's no particular reason that a day with a little fun in it would be more productive than a day of focused, serious work. Practically, we all know that we're more likely to be productive if we're having a little fun mingled into our task focus. How does that work exactly?
First, it helps us remember that people are not computers and they don't work the way computers do. Our thinking is a complex weaving of reason and memory and sensory awareness and emotion. Fun can involve three of those, and that means that it's actually quite a rich form of thinking. A little fun is likely to be using a lot of your brain, and that wakes up more resources for applying to your work.
Next, it's useful to think about the patterns in your thought and work. Patterns work the same way over and over. Real productivity involves doing more than repeating the same patterns: it involves creating new connections. This happens naturally when these patterns are disrupted. Fun is often a pleasant way to interrupt an active pattern so there's room for change.
Finally, we can think about the role of fear or anxiety in our productivity. While people often assume that fear must be a good motivator (it only seems logical), in actual fact we all know the moment when terror stops us from thinking or moving. Fun is a prophylactic against paralyzing fear: when we have fun, we convert the fear into exhiliration, or we deflate it into irritation. Either way, we are free to move.
So if it's really important that you are productive at work, find the spaces in the day that allow for a little fun. Then make it happen.