The CD-i is
most definitely a video game console - at the absolute worse it's a multi-purpose device, one of the purposes is being a console. If something plays games, has controllers and isn't a PC, it's totally a console. Even the
"remote" controller has a pseudo-joystick on it - the device is
clearly gaming-oriented and it was advertised as such, or rather, as a
"media player which plays games".
In fact,
games is the first thing the advert mentions. I quote:
"the ultimate in games, video, music and more". It's not directly referenced as a console because the image of a console back then was
"a thing that plays games", the CD-i was offering
"more than that", not to mention that CD's were all the rage, so instead the term
"CD player of the next generation" is used. For all intents and purposes though, by today's standards of what a console is
(entertainment hub with a focus towards games), the CD-i is a console, point.
For similar reasons the NES is called the
"Nintendo Entertainment System" while the Japanese Famicom actually means
"Family Computer" - the term
"computer" was avoided in America due to a recent industry crash and Nintendo of America wanted their system to be associated with toys, not computers. It's all a matter of marketing.