No, it is absolutely not mandatory for you to comment or create threads on any or all of the blogposts of your Inviter. It is only his special request to you to visit his blogposts and share your comment.
If you do not respond to the invitation, it will not make any harm, either to you or him.
But, if you respond by visiting his blogposts you will be more beneficial than him. In addition to extra Bin Points, you may get some resourceful information from his blogposts or get some insight to improve and monetize your blog. Responding to an invitation makes your profile more richer and it will help you to attract more invitations in future, which will, of-course, save your time to become an "Influencer".