The video game arcade grew out of earlier electromechanical amusements, primarily pinball(which has had a small renaissance in the US). The joy of pinball is a combination of "bright lights and chimes" - attractive theming giving it a monumental feel, the physics of the game being complex and chaotic, and a "beat the operator" element of skill where good players can play for longer and are even rewarded with more credits. Every time you come in to play a pinball, it's slightly different because the parts were readjusted or the ball had grown worn.
When video arcades started to grow popular at the end of the 1970's, they retained most of these elements: An arcade game was a "destination" for game enthusiasts and had the best technology available at the time. They didn't have real physics like pinball, but they were very reliable, giving the skill element a new wrinkle - the operator mostly wasn't a factor, so you played against the game design as the developer intended. While free credits for high scores were eliminated, time extension was still a common part of the gameplay. Playing for high scores or going longer on one credit are the underlying factor to being "into" arcade games - they are fundamentally short "instant fun" experiences and you have to fight them to get more out of your credit.
There's a strong element of "performing" an arcade game - not just consuming it but making the most of every nuance. Not all arcades are designed fairly, but the best ones allow you to clear the game on one credit if you are very good. It can be very satisfying to spend time practicing an arcade and then be able to perform it again on demand.
While consoles got better and closed the gap on technology, the arcade got a second wind in the 90's as fighting games and larger format games like Daytona USA became central, preserving the monumentality of it and opening up more multiplayer experiences, which helped the arcade retain a social feeling.
Since video games are so prevalent now, and allow for cheaper, longer-format and less intense experiences, arcades have become a niche, but their style of gameplay remains popular.