Simple Circular Words

Perl 6, 46 bytes

{!/[(.).*]**4<?{[+^] $0 Xeq[...] ~<<$0[^2]}>/}

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A regex solution that finds if there are four characters in the string such that the two later characters are in different sections of the circle, as defined by the first two characters.

Explanation

{                                           }   # Anonymous code block returning
 !/                                        /    # If the input does not match
   [(.).*]**4                                     # Any 4 characters
             <?{                          }       # Where
                           [...]                    # The range from
                                 ~<<$0[^2]          # The first character to the second
                        Xeq                         # Contains which of  
                     $0                             # The four characters
                [+^]                                # Reduce the list of booleans by xor
                 # Effectively, if only one of the 3rd or 4th character is in that range

K (ngn/k), 26 24 bytes

{&/|/x=&\'x:-:\|26!x-*x}

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*x first letter of the argument x

x- subtract it from each of x as ascii code

26! mod 26

| reverse

-:\ make a pair of the list and its negation

x: assign to x

&\' cumulative minima and maxima (max is min under negation)

|/x= boolean mask for where x[i] is the current minimum or maximum

&/ all (and-reduce)

05AB1E, 14 13 bytes

Fixed a bug thanks to NickKennedy

Ç.sεć-ć/ï_Ë}P

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Ç               # convert each letter to its codepoint
 .s             # suffixes of this list
   ε       }    # for each suffix:
    ć-          #  subtract first from others: [b-a, c-a, d-a, ...]
      ć/        #  divide others by first: [(c-a)/(b-a), (d-a)/(b-a), ...]
        ï       #  round down
         _      #  compare with 0
          Ë     #  all equal?
            P   # after the loop, product (1 iff the list is all 1s)