What does "like kicking a puppy" mean?

The phrase "kicking a puppy" means that the action would be picking on/bullying a weaker target.

So in this case, Zemlin does not care about Microsoft because to them Microsoft is a very weak and easy target and to harm them (kick them) would be like "kicking a puppy" i.e. picking on something that cannot defend itself.

Basically it's an insult, they are implying that Microsoft is so small and helpless that it's beneath them to even bother with them.

I think an adequate simile would be "like taking candy from a baby", if you're more familiar with that.

Something which is 'easy' (physically if not emotionally), implicitly mean or unfair to the subject.