You may have noticed a superficial similarity between the different parts of the manuals and the different parts of the games. However, the analogous parts have different relative canonicities, so a comparison of each aspect outlining the differences is useful.
When comparing the text of the game with the text of its corresponding manual, the text of both should be consistent with each other, since each has the same purpose and similar canonicity. I've never encountered serious inconsistency between game and manual, and I believe that they both have the same relative canonicity. Thus, one doesn't override the other has evidence; both have equal weight.
The only inconsistency one could possibly find is with what certain characters say. For example, in the OoT manual the Deku Tree says something different than what he says in the game. Which one is more canonical? The answer is that they are equally authoritative. Remember that the purpose of the text is to present the history of Hyrule, not to give exact quotes of what specific people said. As long as both convey the same general idea (in the Deku Tree's case: "I've been cursed, it is your destiny to save Hyrule, here is the Kokiri's Emerald"), both quotes are valid interpretations of what might have really been said.
To summarize, the text of both a game and its manual can be quoted with equal confidence in their validity.
The images of the manuals and the imagery of the game both fall into a generalized category of "artwork." The relationship between the artwork of a game and its manual is a little different than that of text.
First of all, there is the obvious fact that manual artwork is more detailed than game artwork. This is because manual artwork is hand-drawn and game artwork is rendered with pixels or polygons. This allows manual artwork to give a better approximation of the real Hyrule. Thus, in general, manual artwork has more authority than game artwork, by virtue of looking better.
However, manual artwork is usually limited to character and item artwork, along with a few scenes. Game artwork is more expansive, giving a fuller experience. Games expand the artwork to levels not explored by the manual, such as more enemies and renderings of locales (like specific deserts and mountains, as opposed to general scenes). This makes game artwork crucial evidence also.
There are sometimes inconsistencies between game and manual artwork, so how do we resolve these? For example, in the ALttP manual Agahnim wears a red cape, while in the game he wears green. I would consider the manual artwork to be more canonical, since it gives a better approximation. The in-game Agahnim may have been limited by engine restraints, so he may not be represented with complete accuracy. In general, I defer to the manual's judgement on artwork matters.
In some cases, manual and game artwork can interfere with each other. An example already discussed is the artwork in the LoZ manual. Link's character art (and probably also the enemy art) seems to be based on the game artwork, not the imagery of the real Hyrule. This reduces the validity of the manual artwork, since it reflects the game artwork, not the true imagery of Hyrule. But because the manual art is more detailed, it is still more canonical than the game artwork.
The lesson here is to be careful and to not get stuck in a rigid methodology (as in always rejecting game art in favor of manual art regardless of the circumstances). Be flexible and let your common sense do the judging.
There's actually no relationship between the gameplay of the games and the gameplay instructions of the manuals. These are two different things. The manual isn't a game, so there is no gameplay in a manual. However, if we're talking about gameplay instructions, which appear in both games and manuals, I consider both to be equally noncanonical. After all, who cares if you have to press button A?
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