Jelly, 17 12 11 bytes

ẆmþJẎ“£uƇ»e

Try it online!

-5 bytes by adapting emanresu A's approach
-1 byte thanks to ovs!

How it works \$\le\$

ẆmþJẎ“£uƇ»e - Main link. Takes a word W on the left
Ẇ           - Contiguous substrings S of W
   J        - Yield the range 1 ≤ i ≤ len(W)
  þ         - For each pair (S, i):
 m          -   Take the ith elements of s
    Ẏ       - Tighten into a list of strings
     “£uƇ»  - Compressed string; "nice"
          e - Is this in the list of strings?

Jelly, 17 12 11 bytes

ẆmþJẎ“£uƇ»e

Try it online!

-5 bytes by adapting emanresu A's approach
-1 byte thanks to ovs!

How it works

ẆmþJẎ“£uƇ»e - Main link. Takes a word W on the left
Ẇ           - Contiguous substrings S of W
   J        - Yield the range 1 ≤ i ≤ len(W)
  þ         - For each pair (S, i):
 m          -   Take the ith elements of s
    Ẏ       - Tighten into a list of strings
     “£uƇ»  - Compressed string; "nice"
          e - Is this in the list of strings?

Jelly, 17 12 bytes

ẆµmJ)Ẏ“£uƇ»e

Try it online!

-5 bytes by adapting emanresu A's approach

How it works

ẆµmJ)Ẏ“£uƇ»e - Main link. Takes a word W on the left
Ẇ            - Contiguous substrings of W
 µ  )        - Over each substring S:
   J         -   Yield the range [1, ..., len(S)]
  m          -   For each i in the range, take the ith elements of s
     Ẏ       - Tighten into a list of strings
      “£uƇ»  - Compressed string; "nice"
           e - Is this in the list of strings?

Jelly, 17 12 11 bytes

ẆmþJẎ“£uƇ»e

Try it online!

-5 bytes by adapting emanresu A's approach
-1 byte thanks to ovs!

How it works \$\le\$

ẆmþJẎ“£uƇ»e - Main link. Takes a word W on the left
Ẇ           - Contiguous substrings S of W
   J        - Yield the range 1 ≤ i ≤ len(W)
  þ         - For each pair (S, i):
 m          -   Take the ith elements of s
    Ẏ       - Tighten into a list of strings
     “£uƇ»  - Compressed string; "nice"
          e - Is this in the list of strings?

Jelly, 17 bytes

ẹⱮ“£uƇ»ŒpIµEaAƑ)Ẹ

Try it online!

How it works

ẹⱮ“£uƇ»ŒpIµEaAƑ)Ẹ - Main link. Takes a word W on the left
  “£uƇ»           - Compressed string; "nice"
 Ɱ                - For each character c in "nice":
ẹ                 -   List the indices of c in W
       Œp         - Cartesian product of the lists of indices
         I        - Forward differences of each
          µ    )  - Over each:
           E      -   Are the all equal?
             AƑ   -   Are they all positive? (lit: all invariant under absolute value)
            a     -   Both are true?
                Ẹ - Are any true?

Jelly, 17 12 bytes

ẆµmJ)Ẏ“£uƇ»e

Try it online!

-5 bytes by adapting emanresu A's approach

How it works

ẆµmJ)Ẏ“£uƇ»e - Main link. Takes a word W on the left
Ẇ            - Contiguous substrings of W
 µ  )        - Over each substring S:
   J         -   Yield the range [1, ..., len(S)]
  m          -   For each i in the range, take the ith elements of s
     Ẏ       - Tighten into a list of strings
      “£uƇ»  - Compressed string; "nice"
           e - Is this in the list of strings?