Just so you’re made aware, it is indeed against the EULA.
Cloud Computing: Subject to 1.B.vi hereof, use the Platform, including a Game, in connection with any unauthorized third-party “cloud computing” services, “cloud gaming” services, or any software or service designed to enable the unauthorized streaming or transmission of Game content from a third-party server to any device. For the avoidance of doubt, this Section 1.C.v does not prohibit the use of any service that has been authorized by Blizzard.
Now, if it something that has been authorized by Blizzard, would most likely be companies such as NVidia’s GeForce Now.