What is a Quest Word™?

Question

_{In the spirit of the What is a Word™/Phrase™ series started by JLee, a special brand of Phrase™ and Word™ puzzles.}

The quest Ryan was on brought him to the final clue he needed: "If a word conforms to a special rule, I call it a Quest Word™.
Use the examples below to find the rule."

$$ % set Title text. (spaces around the text ARE important; do not remove.) % increase Pad value only if your entries are longer than the title bar. % \def\Pad{\P{0.5}} \def\Title{\textbf{ Quest }} % \def\S#1#2{\Space{#1}{20px}{#2px}}\def\P#1{\V{#1em}}\ \def\V#1{\S{#1}{9}} \def\T{\Title\textbf{Words }^™\Pad}\def\NT{\Pad\textbf{Not}\T\ }\displaystyle \smash{\lower{29px}\bbox[yellow]{\phantom{\rlap{rubio.2017.02.04}\S{6px}{0} \begin{array}{cc}\Pad\T&\NT\\\end{array}}}}\atop\def\V#1{\S{#1}{5}} \begin{array}{|c|c|}\hline\Pad\T&\NT\\\hline % \text{QUEST}&\text{ADVENTURE}\\\hline \text{TRIANGLE}&\text{SQUARE}\\\hline \text{ESTABLISH}&\text{CREATE}\\\hline \text{STRENGTH}&\text{INTELLECT}\\\hline \text{QUESADILLA}&\text{ENCHILADA}\\\hline \text{EQUALITY}&\text{CORRUPTION}\\\hline \text{TRIPLE}&\text{DOUBLE}\\\hline \text{STRIPES}&\text{DOTS}\\\hline \text{PEDESTRIAN}&\text{WALKER}\\\hline \text{QUEUES}&\text{LINES}\\\hline \text{SEQUITUR}&\text{SENSIBLE}\\\hline \text{PEST}&\text{NUISANCE}\\\hline \text{PROTEST}&\text{ACTIVISM}\\\hline \text{ASTRONOMY}&\text{STARGAZING}\\\hline \text{ASTROLOGY}&\text{HOROSCOPE}\\\hline \text{TRIAGE}&\text{PRIORITIES}\\\hline \text{EQUIPMENT}&\text{WEAPONS}\\\hline \text{CHEQUES}&\text{BILLS}\\\hline \text{RESTRAINT}&\text{FORWARDNESS}\\\hline \text{TRIM}&\text{HAIRCUT}\\\hline \end{array}$$

CSV Version:

QUEST,ADVENTURE
TRIANGLE,SQUARE
ESTABLISH,CREATE
STRENGTH,INTELLECT
QUESADILLA,ENCHILADA
EQUALITY,CORRUPTION
TRIPLE,DOUBLE
STRIPES,DOTS
PEDESTRIAN,WALKER
QUEUES,LINES
SEQUITUR,SENSIBLE
PEST,NUISANCE
PROTEST,ACTIVISM
ASTRONOMY,STARGAZING
ASTROLOGY,HOROSCOPE
TRIAGE,PRIORITIES
EQUIPMENT,WEAPONS
CHEQUES,BILLS
RESTRAINT,FORWARDNESS
TRIM,HAIRCUT

The puzzle satisfies the series' inbuilt assumption, that each word can be tested for whether it is a Quest Word™ without relying on the other words.

These are not the only examples of Quest Words™, many more exist.

Answer 1

A Quest Word™ ...

... contains at least one of the contiguous three-letter substrings of the word EQUESTRIAN: EQU, QUE, UES, EST, STR, TRI, RIA or IAN. Not Quest Words™ don't contain any of these three-letter sequences.

Evidence section:

[QUE]ST            ADVENTURE
[TRI]ANGLE         SQUARE
[EST]ABLISH        CREATE
[STR]ENGTH         INTELLECT
[QUE]SADILLA       ENCHILADA
[EQU]ALITY         CORRUPTION
[TRI]PLE           DOUBLE
[STR]IPES          DOTS
PED[ESTRIAN]       WALKER
[QUE][UES]         LINES
S[EQU]ITUR         SENSIBLE
P[EST]             NUISANCE
PROT[EST]          ACTIVISM
A[STR]ONOMY        STARGAZING
A[STR]OLOGY        HOROSCOPE
[TRI]AGE           PRIORITIES
[EQU]IPMENT        WEAPONS
CH[EQU]ES          BILLS
R[EST]RAINT        FORWARDNESS
[TRI]M             HAIRCUT

They are called Quest Words™, because ...

... "equestrian" has a quest in it, obviously.