Is there any way to get Email Client Usage data through the API? I didn't see anything either under Subscribers or Campaigns.
Unfortunately the Email Client Usage data isn't available through the API at this stage, but I've added your vote for this as something we'll consider for future updates. I agree it would make for a nice addition.
For now, this data is only available in your account.
You can catch today's API updates announcement over at the API Announcements forum topic.
Hope that helps.