A video game or movie logo is always tough to figure out. Video games, more so. And to take an existing franchise and try to create a logo in that same light is even more challenging.
I think the artist has done a decent job here. The biggest concern would definitely be the treatment of typography. While even the professional industry doesn't always make good type decisions, it's still important to make sure those decisions are made correctly. It's almost always a bad idea to take a serif font and add any amount of bevel or emboss. Also, outlining text should be done in a way that aids reading.
The illustrations here are quite nice, though I feel they are so complicated that one has trouble interpreting what they are. One should always be careful not to overdo layer styles or effects. A simpler design says more about professionalism than throwing on as many flashy effects as possible.
Another concern is the fact that the logos are highly monochromatic. Summoners Symphony does much better with it, but the other logos have the word "Zelda" in the same hue as the background objects, which creates less contrast: something of utmost importance when it comes to readability.
I understand that it may not be artist's intention to imitate the visual conventions of existing Zelda logos. Therefore, the fact that these logos have a much different feel than the official logos isn't necessarily a problem.
In summary, the biggest issue is typography: contrast of letters against the background, simplicity of design, and perhaps the appropriateness of the modern scrawl in the subtitles.
Take all of these into account, and your logos will go from being just more fan-made Zelda logos to something that will make your audience think twice.
Hope this has been constructive!
This was an excellent way to critique one's fundamentals about logo designs. The standards are challenging enough as it is according to the star scales, but luckily enough, you have the well-constructed, elaborate details to specify precisely what flaws are mainly concerned of from this picture containing the Zelda logos. The construct and elaboration is easy and clear to understand from here, and towards the end, it's also encouraging by the likes of advices being taken into account. Thank you for your sophisticatedly analyzed critique!