The importance is overstated more often than understated. Importance "amount" is a relative term.
The latest games are designed for strong graphics processors, and strong graphics processors have their own page buffer, which is what video memory is used for. Integrated Intel and AMD graphics is stronger than it used to be, and the system memory, when at least 8GB, has plenty to allocate to the graphics processors. Dedicated GDDR5 type video memory does get about a 25% performance boost over DDR3 memory and maybe 15 to 18% over DDR4. Having enough page buffer for the graphics processor to fill before getting sent to the LCD of course is important. But, the amount of memory required is in what the graphics processor can make good use of, and also related to the game settings and display resolution.
This is a table of graphics processors to gaming performance:
https://www.notebookcheck.net/...849.0.html
Guild Wars 2 is a year 2012 game. The Hearthstone games are low system requirements to play, and even Wildstar in 2014 is not very hardware demanding
http://www.game-debate.com/...e=Wildstar
When gaming is discussed, it is typically 2016 and 2017 released games, and on PC gamers expect better graphics and speed than in a gaming console, as designed into gaming pcs of desktops, or expensive new laptops featuring a GTX 1050 mobility or better.
When you are satisfied at lower frame rates in older than latest releases, powerful hardware is not as important, and therefore the dedicated GDDR5 of high performance graphics cards naturally is not as critical.
The CAN I RUN and Systems Requirements Lab match against game designers instead of the actual play and extrapolated and interpolated data of Notebookcheck based on real gaming reports.
So, just as some people think in terms of high performance cars, fine wines, premium beer, and gourmet meals and have an expectation of satisfaction at those levels, most gamers today have an expectation of smooth play at no less than medium settings of all games available to buy or play, and to them, dedicated video memory and decent graphics cards are expected.
That doesn't mean that you can't enjoy more classic gaming at lower settings and frame rates.
As long as you have at least 8GB of system ram, most games will run as playable on even midgrade non-gaming laptops.
Intel HD Graphics 620 of an i3-7100U is at rank 289 in the table, as in the middle.