How can it be a quadruped when it has no legs at all?
it's based off of it's body, large and above "long" types are always considered quadrupeds regardless of how many legs they actually have
May I see the rule that says that?
Bigger and Smaller Creatures: The figures on Table: Carrying Capacity are for Medium bipedal creatures. A larger bipedal creature can carry more weight depending on its size category, as follows: Large ×2, Huge ×4, Gargantuan ×8, Colossal ×16. A smaller creature can carry less weight depending on its size category, as follows: Small ×3/4, Tiny ×1/2, Diminutive ×1/4, Fine ×1/8.
Quadrupeds can carry heavier loads than bipeds can. Multiply the values corresponding to the creature's Strength score from Table: Carrying Capacity by the appropriate modifier, as follows: Fine ×1/4, Diminutive ×1/2, Tiny ×3/4, Small ×1, Medium ×1-1/2, Large ×3, Huge ×6, Gargantuan ×12, Colossal ×24.
Because that is the only text I could find mentioning about large creatures.
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For whatever its worth, the mount for the First Mothers Fang Cavalier archetype has this to say for its serpent mount "A serpent mount is considered to be a quadruped for the purpose of determining its carrying capacity,"
To me, that sort of kind of vaguely implies that a NORMAL giant constrictor snake would NOT be considered to be a quadruped (if it was, why explitly add that clause?). But that line of argument is, IMO, not exactly conclusive
In any case, snakes of size Large and above seem to have "tall" rather than "long" reaches. See the Emperor Cobra and the Giant Anaconda for examples.
The answer to this question is very important to a summoner with a serpentine eidolon.