"Classic" is another buzzword that people use in a futile effort to validate their opinion on an older video game that they have fond memories of, and there is no objectivity to it whether you use it as a noun or an adjective. Majority does not make absolute right, so it's simply another hollow descriptor in a long line of them which people throw around because they want to invalidate the opinion of people who criticise their favourites. Usually people who use this word to describe games take an attack on said game as an attack on themselves...which I suppose to be fair, it usually is, because people just love to throw inflammatory statements around on the internet for no other reason than that they can and not face any repercussions for it.
Maybe that's a cynical perspective, but as someone who played a lot of titles that are regarded as "classic" later in life and didn't see the appeal to them, and a few at the time which I later went back to only to find that my opinion had changed (both for better and for worse!) that is my observation on it. Video games have progressed significantly over the last 25 years in particular, and a lot of games haven't withstood the test of time as well as they might have when compared to more modern titles. Ideas are expanded upon (whether they are improved or not is subject to debate, but they are definitely expanded upon) and there's no denying that technology has improved in leaps and bounds. That doesn't necessarily mean that games have gotten better - hell, I've had more fun on low-spec indies than I have on big budget AAA titles with all the 4K HD 60fps/1080p bells and whistles attached - but there is a noticeable improvement in performance across generations: as the easiest example, compare the gameplay of the core Pokemon titles across consoles and see how much smoother the gameplay generally is.
How to defend against this? Call the old game a classic! Thus, you have an instant defence against any and all criticism...or so many like to think. There is definitely merit to the argument that older games should not be compared to newer ones and found lacking in some departments, because you can hardly fault an old game for being on hardware that cannot capture the intended gameplay experience as well as newer hardware could, but to put it on a pedestal and label it as a "classic" is the height of farce. It's because of things like this that we have series that recycle gameplay over and over and never really improve the way they could if not bound by the idea that they need to copy this "classic" title to be given the time of day, and why new ideas are shunned, or laughed at, or outright hated by many. Nostalgia drives this industry, and the attitude behind calling an old game a "classic" and refusing to hear any more on the matter is at the heart of it. Opinions are opinions. "Classic" is not some magical shield you can use to label differing perspectives as objectively wrong. Good lord.
So, yes. What makes a game a classic is nothing more or less than your personal opinion. And other people sharing it or not sharing it does not change that in any objective way, although it does seem to be that a prerequsite for calling a game this and not being verbally crucified everywhere you go is if the place you go has people who share that opinion. But it's just another opinion the same as anything else, albeit one heavily rooted in nostalgia.