Reactivation campaigns are a great way to keep your database clean. In your example, I really love the use of personalization to remind the inactive user why they should remain an (engaged) customer.
Cute puppies definitely grab attention, but it's important to remember these subscribers have likely not been opening your messages in the first place. Get creative with subject lines and prompt emotional curiosity: "Did we do something wrong"?; "Is is you, or is it me"; "Goodbyes are hard". Once you get them to open, hit them with the engaging graphics and headlines.
Keep it short, simple, sweet. Remind the user why they signed up, clearly sharing the value proposition of your marketing communication. Ideally, build a preference center and allow the subscriber to edit the types of content and frequency of communications.
Litmus had a pretty good example, borrowing from the Clash and using the subject line "Should we stay or should we go?".