Sorry if I don't answer to the full extent of your post. But consider my agreement of including "standing the test of time" in the definition.

Funny thing about Shakespeare: he was considered cheap entertainment for the masses back in his days, just like many other contemporary dramatists. Yet we forgot about all the others, while holding Shakespeare in high regard. His works truly stood the test of time.

I wonder if something like Doctor Strange in the Multiverse of Madness will be talked about in 70 years like we today talk about Casablanca. I kinda doubt it.

Games don't live long enough yet, to give a real insight here. In comparison I think games are at a point where movies introduced color and sound into the technology. So in my opinion at this point games have all the basic technological tools available, that the medium can have (there are always refinements, as were for movies), but games are still in the infancy in regards of exploration how to use the medium. You are right, Tetris lived kinda long, nearly 40 years (1984), so props to Alexey Pajitnow.

You are right, that most games are both, art and an entertainment product. And sadly for most gaming companies they design first fir an entertainment product.

This year we saw some game designers critizice design decisions of Elden Ring, while the game itself became very successful. I think that illustrates the difference perfectly. All these critics had valid criticism if you wanted to make Elden Ring a better entertainment product. Yet it was successful, because in the design of the game art became a much higher priority than in most high profile games of the past few years, so it stood out as much more artful. Don't get me wrong, a lot of design decisions in Elden Ring are still for an entertainment product, but it found a different balance in it's design goals.

As a software engineer myself, I can fully relate to this post. On my shelf resides a book named 'The Art of Computer Programming' by Donald Knuth. I try to follow the principles of Software Craftmanship. There is Perl Poetry, which tries to be functional (being an actual program) while also reads as another artistic meaning.

Games usually try to lean either into being a product (like most AAA) or sometimes into being artistic (some indie games). Usually there is this split in design choices, but an area where I think both are merged well is architecture. In architecture the goal is to have something functional, yet at the same time expressive. Which is great I think. There are few examples that excel at a synthesis of these two in gaming, for me personally A Short Hike and Katamary Damacy come to mind.

Art is something you can take in and appreciate isnt it. For me gaming is an experience, a even higher level than art.

For me no.

I don't stand long enough in a game to admire the surroundings. 

To me it is entertainment.

You are right about Shakespeare.  His plays were cheap entertainment for the masses, and yet there was also more going on underneath that you might not see at a first glance.  For film, I consider the original Star Wars trilogy (from the 1970's & 80's) to be the equivalent of Shakespeare.  Originally these movies were not taken seriously by critics, while they were extremely popular with the mass market.  However, now we look back at them and can see them as classics.

I also agree that games are a young medium.  The first few decades of film were characterized by technological improvements, like sound and color.  Eventually, the market became resistant to the tech improvements that the film industry tried to implement (like 3D and ultra-wide screen formats).  Since the film industry couldn't rely on technological improvements to entice people to the theatres, they started focusing more on telling good stories. I kind of think that the games industry is at this transition point now.  Improvements in technology are at a point of highly diminishing returns.  The studios that will see the most success in the coming years are those who focus on improvements in gameplay much more than improvements in graphics.

You're so fatally wrong about Cinema that I'm wondering if we are even living in the same reality. The only box office hits nowadays are the big budget blockbusters, good graphics and special effects is pretty much the only thing that convince people to take of their butts from their couches and go to theaters. Lower budget movies destiny is streaming, simply because the experience from big screens is far superior on theater compared to home media for blockbusters, but not as much for smaller budget movies. That's why cinema market is plummeting and streaming market is growing.

Gaming is a bit different because you need to be invested in the gameplay for quite a few hours before beating the game. It's something more akin to book series or TV shows, production value can be often overlooked if said thing is fun enough, otherwise you will just drop it. This is even more true in subscription model.

However imo this is a double edged sword. I personally don't think games need to bring immediate pleasure and satisfaction, I appreciate games that take their time to really show their colors, there are some games you need a time to grasp the mechanics and design, and a market that will drop that game to something else because it wasn't fun enough in the first 1 hour is not what I believe to be the best course for gaming, but it is what it is I guess...

This also, opposing to what you seems to think, making gameplay more and more formulaic rather than innovative. That's because is much easier to catch someone showing something a person already like and know than something new, specially when talking about new IPs.

It may not seem very intuitive, but technology in other hand can help to sell a gameplay, because technology itself is exciting, even if the gameplay is not, think about Wii Sports vs Switch Sports.

"You're so fatally wrong about Cinema that I'm wondering if we are even living in the same reality."

We aren't living in the same reality.  I'm talking about technological changes made to the movie theatres themselves (and not the production side).  Since you don't know anything about the history of how the film industry developed you just assumed that I was wrong.

Theatres started as small nickelodeon machines, then used a big screen, then implemented sound, and then added color.  Each of those things required movie theatres to make physical changes to their structures, and all of those changes happened, in total, after about 30 years or so.  Since color was added there have been other technological improvements to movie theatres, some stuck and some didn't.  The main ones that have stuck and been popular are probably surround sound and the IMAX format, so that is maybe 2 major changes in the next 8 decades or so.  (And then there are the 3D format and the ultra-wide screen format which have had limited or no success.) Technological improvements have happened to the movie theatres since the addition of color, but they haven't happened nearly as quickly as those first few decades.  

If you want an analogue to this in gaming it would correlate to buying a new console.  We currently need to upgrade the physical thing that plays the media, just like movie theatres needed to upgrade to play the latest films in sound in those early years.  When I was talking about the game industry reaching diminishing returns with technology, I referring more to the technology that we buy and then bring into our home (i.e. the console).

If you want to talk about the production side of film making then that would correlate to the production side of game development, and even then the budget is spent fairly differently between these two media.  For AAA games the biggest chunk does go toward art and graphics.  However, for some really big budget films the biggest chunk actually goes toward paying the actors and director.  Robert Downey Jr alone got $20 million up front for doing Avengers Endgame (plus a percentage of the box office), and there are a whole lot of other big name actors in that film as well.  On top of that modern digital effects in film are really just a different way of skinning the same cat.  Now people use digital effects when in the past they would build sets, or use puppets or use other practical effects (depending on what you are talking about).  It's not the digital effects themselves that are the draw so much as the big budget.  For example, the Lord of the Rings films built real sets while the Star Wars prequels made all of their settings in CGI.  Both trilogies came out around the same time, and most people seemed to prefer the Lord of the Rings trilogy.  It wasn't the new technology that was the draw, so much as the raw amount of money spent creating the fantasy worlds in these films.