Is the word typeable with keys adjacent to each other?

Pyth, 66

?"Yes".Am>2sm^-.uk2Cm.Dx"qwertyuiopasdfghjkl*zxcvbnm"b9.5dC,ztz"No

Try it here.

I was surprised to learn Pyth doesn't have a hypotenuse function, so this will likely be beat by a different language. I'll propose a hypotenuse function to Pyth, so this atrocity won't happen in the future.

Explanation

I transform the keyboard into this:

┌───┬───┬───┬───┬───┬───┬───┬───┬───┬───┐
| Q | W | E | R | T | Y | U | I | O | P |
└─┬─┴─┬─┴─┬─┴─┬─┴─┬─┴─┬─┴─┬─┴─┬─┴─┬─┴─┬─┴─┐
  | A | S | D | F | G | H | J | K | L | * |
  └─┬─┴─┬─┴─┬─┴─┬─┴─┬─┴─┬─┴─┬─┴─┬─┴───┴───┘
    | Z | X | C | V | B | N | M |
    └───┴───┴───┴───┴───┴───┴───┘

Which I then encode as "qwertyuiopasdfghjkl*zxcvbnm". Then I used divmod with modulo 9.5 to figure out the 2D coordinates of every key. Then I compute distances between consecutive keys, and check if the squared distance < 2.

CJam, 83 75 74 bytes

l_1>]z["qwertyuiop asdfghjkl  zxcvbnm "[__B>]z+s_W%+_]zsf{\#)}:*"Yes""No"?

Try it online.

Explanation

The general approach is to produce a big adjacency string containing every pair of adjacent keyboard characters and then check that every pair of adjacent input characters is contained in that string.

I'm quite happy with how I managed to build the adjacency string, which uses very simple and compact logic.

l_1>]z          "Read a line of input and create a list of every pair of
                 adjacent input characters. There will be a trailing element
                 of just the final character, but that's okay since any single
                 lowercase letter can be found in the adjacency string.";
["qwertyuiop asdfghjkl  zxcvbnm "
              "^ Create the in-row forward adjacency string.";
[__B>]z         "Create the alternating-row forward adjacency string by
                 interleaving the in-row string with a substring of itself
                 starting with the middle row letters:
                   'q w e r t y u i o p   a s d f g h j k l  zxcvbnm '
                 + ' a s d f g h j k l     z x c v b n m  '[no interleave here]
                 -----------------------------------------------------
                   'qawsedrftgyhujikolp   azsxdcfvgbhnjmk l  zxcvbnm '";
+s              "Append the alternating-row forward adjacency string to the
                 in-row forward adjacency string.";
_W%+            "Append the reverse of the forward adjacency string (the
                 backward adjacency string) to the forward adjacency string.";
_]zs            "Double every character in the adjacency string so every
                 character is adjacent to itself.";
f{\#)}          "Map each pair of input characters to its 1-indexed location in
                 the adjacency string (0 if not found).";
:*              "Calculate the product of each pair's location in the adjacency
                 string. This will be nonzero if and only if every pair of
                 input characters are in fact adjacent.";
"Yes""No"?      "If the product is nonzero, produce 'Yes'; otherwise, produce
                 'No'.";
                "Implicitly print the result.";

J, 77 bytes

No`Yes{::~[:*/2>+/"1@(2|@-/\3(|,.<.@%~+-:@|)'qazwsxedcrfvtgbyhnujmikXolX'i.])

Usage:

   f=.No`Yes{::~[:*/2>+/"1@(2|@-/\3(|,.<.@%~+-:@|)'qazwsxedcrfvtgbyhnujmikXolX'i.])

   f 'redresser'
Yes
   f 'qwergy'
No
   f 'ppcg'
No

Method:

For every input letter I generate it's 2D coordinate (similar to the image in the question) based on it's index in the string 'qazwsxedcrfvtgbyhnujmikXolX'. For every pair of letters in the input I check if their coordinates' Manhattan-distance is smaller than 2. If all are, I output Yes, No otherwise (by abusing the ` operator).

Try it online here.