The URL you are using is returns a different type of content based on the Accept
header of the request.
In Chrome a response with a "Content-Type" header of "text/html". Which is surprising given the .gif
suffix on the URL.
Chrome accept headers look like: Accept:text/html,application/xhtml+xml,application/xml;q=0.9,image/webp,*/*;q=0.8
However if I use curl -I http://media.giphy.com/media/zl170rmVMCpEY/giphy.gif
I get Content-Type: image/gif
If you look at the image URL on the HTML page, in Chrome, it is actually: https://i.giphy.com/zl170rmVMCpEY.webp
webp is an alternative format to gif, I suspect it is served instead of gif if the browser supports it.
If Twilio supports webp format images you could use that instead.
Gify also seem to use mp4 format, it looks like they brand as gif, but don't actually serve gif's to clients which can accept HTML or WebP content.