Games, drinks, children, etc. are diversions from the activities of software development and business which the employer is paying you to engage in on their behalf.
Participating in them outside of office hours would tend to _increase_ your productivity at work by giving your head a rest.
Our most productive employees are the ones without kids, families or bustling social lives. And those same employees are the ones who are working on "side" projects while they are also working for us.
Any company that would tell an employee that they can't work on a side project, either as a business or a hobby that is not in direct competition with that company is setting itself up for failure because it's a sign of a larger cultural issue within the company itself, stemming from severe mismanagement.
"Side projects" and open-source projects are great for self-education. I've nothing but good things to say about them for employee improvement.
Running a separate business is a different story altogether. Do you really have productive employees who are operating software development companies on the side? If you do, I can guarantee their primary attention does not lie with you (even though their primary income is being paid by you).
This, I think, is the key distinction. Running a business is a whole lot of work, and much of that work does not make your guy a better software developer. Running a side business is probably going to diminish a programmers productivity.
Writing an application (and ignoring the business and customer service side of things) likely will make your programmer more productive, 'cause he learns all this new stuff.
Participating in them outside of office hours would tend to _increase_ your productivity at work by giving your head a rest.