The first linked image's resolution is 1150x612, and the absolute minimum width and height (although ideally images will be larger than this) are 1000x700; this image's height is insufficient. Technically speaking, though, its aspect ratio (the ratio of width to height) isn't a problem. Also, unfortunately, it has more than its fair share of jpeg_artifacts...

Kona's absolute minimum required AR is 1.1:1 according to the Upload Guidelines but images with that low of an AR will rarely if ever be approved by moderators. In my experience, images between 1.2:1 (e.g. 6:5) and 1.25:1 (e.g. 5:4) AR might be evaluated more harshly before being approved but will generally fare fine if they lack other problems. Securing approval on anything between 1.2:1 and 1.1:1 is a longshot at best, and the closer to 1.1:1 you go the more unlikely it becomes.

Anything above 1.25:1 won't have issues in this regard (at least not based on its AR) unless perhaps if it's excessively wide (to the point where it would be impractical to use as a desktop background even with 2 or 3 linked monitors).

Your second linked image (original size 1200x761) fulfills both the minimum resolution and minimum AR requirements even without using waifu2x.