A "petty battle against CloudFlare DNS users"? No. They require a standardized DNS extension in order for their services to operate properly, and CloudFlare is waging a petty battle against the standard.
A "extension" is by definition something they do not require, since otherwise DNS clients written before that extension would not be able to interoperate with them. That's what makes it a "extension" rather than a unconsionable violation of backwards compatiblity.
And that particular extension exists solely as means for DNS proxies to violate the privacy of their users by leaking client identity data to upstream DNS servers. There are several reasons why Cloudflare is evil and needs to die (especially ReCaptcha and associated attacks on TOR), but archive.is is firmly in the wrong on this particular point.