Unfortunately, ESPN does not offer a setting for minimum games or innings pitched. I emailed Customer Service with the same question, in fact.
ESPN Customer Service wrote:Sorry about the confusion for starting pitching limits.
In ESPN Fantasy Baseball leagues, we do not have a way that you may set
a minimum amount of pitching as a limit for either a Rotisserie league
or a Head-to-Head league.
Of course, your league can always pass a rule regarding game/inning minimums. Just be very clear about the requirements and the consequences for falling below the minimum. Then, the commissioner can enforce the rule and administer any penalties manually. An automated system would be preferable, but manual enforcement is not particularly tedious for a rule like this.