Well the second image you provided is the Photo icon for the Photo app, it's like that on my computer too and I have a 1080p monitor that's only a few years old. So as far as that is concerned, that is MicroSoft's low detail icons at work. The first image, it's really subjective, since it's so blown up. If you blow up anything like that, it's going to look pixelated.
Pixelation as you've shown is subjective. It is dependent upon the resolution versus screen size, and how close you sit to your monitor and how good your eyes are. For instance if you have two 1080p TVs fed with the same signal source all else being equal. If you sit the same distance from both and the only difference is the size of the screen, the larger one is going to seem more pixelated.
So as far as a fix for your monitor, the only option is to sit further away from it I'm afraid. If that doesn't work for you, then you could get a higher resolution monitor. My suggestion here is if you go 1080p, don't go bigger than 24" as those that are 27" may seem too pixelated if you are sensitive to that. If you want something larger, then consider getting a screen with a resolution of 1440p. The latter choice is going to be pricier of course.
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