Yes, you can upgrade the display panel to one with higher spec. If it has exactly the same physical dimensions, exactly the same connector type and pinout, and the same (or similar) connector location. "15.6-inch" is a fairly standard size but if the replacement part has any difference in physical height, width, or thickness then it simply may not fit within the plastic chassis. You might be able to get away with filling, filing, cutting, or shaping interior chassis plastics if necessary - a little - but it's delicate and tedious work and it presents many little risks which can add up to the whole project going awfully wrong.
If you want to upgrade the display panel then you should first identify the exact manufacturer, brand, and part number of your existing panel - only then can you compare the specs vs other display panels. Again, "15.6-inch" is a generic descriptor, not a perfectly technical one, there can be significant variations between "15.6-inch" parts.
The replacement panel in your link appears to have the same specs as the original panel, it looks like a suitable replacement but it doesn't look like an upgrade.
And, of course, if you install a screen with higher resolution then you'll get more image quality but less performance in gaming, the GPU has limits on how many pixels it can render each second. You may also have to reinstall or reconfigure GPU drivers, I don't think that should be much of an issue (it should just autodetect and automagically configure itself for you) ... but it could prove impossible to run nonstandard configurations on your specific laptop and thus be the deal breaker.
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