No. Everything you'd consider a computer in this context can do graphics, but they're running the graphical processing through the CPU, which is not optimized for graphical processes and is not performing other functions while it's spending time on graphics.

Even if they advertise a "newer optimized onboard graphics" package, it's nothing compared to the optimization of changing the chip's design. You simply can't optimize graphical processes through a CPU in the same way you can optimize them by changing the design of the CPU to that of a GPU. The rest of your processes will suffer if you ONLY have either. You need both.

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What you're missing is that I have never mentioned gaming once in relation to a graphics card, and yet you can't shake the notion that a graphics card is for gaming. Windows uses heavy graphics. For all the solid colors of the Windows 3.1 days to be lovely shaded transitions we see today takes a lot of graphical processing. Just to have the window frame part of each window is taxing your graphical abilities.

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Do me a favor: Take your current laptop and go into the Windows settings and set everything to lowest quality, no shading, no animations, set it "Windows Classic" look as far back in the history of Windows looking old school as you can go.

I can almost guarantee that you are now experiencing a computer that feels every bit as fast as the one you want to buy to replace this machine. All we changed was Windows settings, not anything within the actual programs you want to run in those windows. All we changed in those settings was to stop sending "extra" graphical processes to your CPU, see?

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Please hear me that graphics card = not only for games.

As was stated earlier in this thread, graphics aren't the only processes which are better optimized as parallel processes. More and more, other programs are utilizing that GPU for non-graphics tasks which, again, are reducing the load from your CPU and making your computer faster at the things that "feel laggy" sometimes.