They don't have a "moat" though - no cutting-edge technology or even content licenses (it's all stolen). Anyone can build their own alternative to it very easily and I'm confident it'll quickly happen to any company that competes with and/or feels threatened by Facebook.
Err, no. This is a serious underestimation of the difficulty involved in acquiring users. Networks effects are a moat. Market share can be a moat.
You don't need to just "build your own alternative to it." You need to get all the content (this is actually not as easy as you make it seem - stolen or not), then integrate that into Instagram, WhatsApp, Slack, and hundreds of other platforms across the world as the supported way of sharing gifs. Then you'll have to build a brand around the product that people remember, and whose website they actually visit when they want images and aren't using one of the hundreds of platforms that already natively integrates giphy.
And in order to do all that, you'll have to somehow manage to convince everyone out there that your gif search system is better than their gif search system that they already know, are comfortable with, and generally happy with. Your pitch will probably be that theirs is owned by Facebook, and is therefore a violation of their privacy. But you know who else is owned by Facebook? Facebook. And yet Facebook is pushing close to 2 billion daily active users.
Convenience trumps privacy in modern society most of the time. I'm sure there will be a changing of the winds - there always is - but there likely will not be significant competition for Facebook/Twitter/Instagram/Giphy/Google/(put any other company in here) until that comes. The network effects are too strong, and the convenience is too great.
There are so many posts about "(Twitter/Facebook/Giphy) clone in a (day/weekend/week/month)" and yet there's a distinct lack of commercial successes in these spaces.