AngularJs Basic Setup (source: http://jsfiddle.net/vjow04jj/1/)

fiddle.css

body{
  margin: 10px;
}
.warning {
  background: #d56c61;
}

td {
  border: 1px solid #ccc;
  height: 30px;
  vertical-align: middle;
  width: 30px;
  text-align: center;
}

td.highlight {
  background: yellow;
  font-weight: bold;
}

fiddle.html

<div ng-controller="wordsController">
  <h2>Find word</h2>
  <input type="text" placeholder="Enter a word" ng-model="word" ng-class="{warning: wordNotFound()}" size="30">
  <table>
    <tr ng-repeat="line in matrix track by $index" ng-init="lineIndex = $index">
      <td ng-repeat="column in line track by $index" ng-init="columnIndex = $index" ng-class="{highlight: isHighlighted(lineIndex, columnIndex)}"
        ng-bind="column"></td>
    </tr>
  </table>
</div>

fiddle.js

var app = angular.module("myApp", []);

app.controller('wordsController', function ($scope) {
  $scope.word = '';
  $scope.matrix = [
        ['d','e','j','s','y','w','y','i','n','l'],
        ['g','j','g','j','p','m','y','e','t','y'],
        ['e','g','w','g','r','e','z','h','g','v'],
        ['y','a','e','p','m','a','m','y','w','b'],
        ['f','d','y','o','d','x','u','f','a','z'],
        ['i','n','s','c','n','w','f','x','t','r'],
        ['x','b','a','k','t','i','e','f','n','s'],
        ['j','d','j','o','u','o','w','r','o','q'],
        ['c','s','w','j','s','e','y','h','y','q'],
        ['d','l','r','k','n','k','y','v','h','n'],
        ];

  $scope.wordNotFound = function () {
    return $scope.word && !$scope.found;
  }

  $scope.isHighlighted = function (line, column) {
    var isHighlighted = false;
    if (highlights && highlights.length) {
      highlights.forEach(function (letter) {
        if (letter.pointX == line && letter.pointY == column) {
          isHighlighted = true;
        }
      });
    }
    return isHighlighted;
  }

  var highlights = [];

  $scope.$watch('word', function (newValue) {
    highlights = [];
    if ($scope.word) {
      $scope.found = true;
      hasWord($scope.word);
    }
  });

  var hasWord = function (word) {
		var letters = word.toLowerCase().split('');
    var currentLetterIndex = 0;

    var isArround = function (pointX, pointY, x, y) {
    	if (pointX == x && pointY == y) {
	      return false;
      }
      if (pointX == x || pointX == x - 1 || pointX == x + 1) {
        if (pointY == y || pointY == y - 1 || pointY == y + 1) {
          return true;
        }
      }
      return false;
    }

    var findLetter = function (letter, pointX, pointY) {
      var out = null;
      $scope.matrix.forEach(function (line, indexLine) {
        line.forEach(function (column, indexColumn) {
          if (!out && column == letter) {
            if (!out && (pointX == null && pointY == null) ||
              (pointX >= 0 && pointY >= 0 && isArround(pointX, pointY, indexLine, indexColumn))) {
              out = {
                letter: letter,
                pointX: indexLine,
                pointY: indexColumn,
              };
            }
          }
        });
      });
      return out;
    }

    var lastX, lastY;
    letters.forEach(function (currentLetter, indexLetter) {
      var hasLetter = findLetter(currentLetter, lastX, lastY);
      if (hasLetter) {
        lastX = hasLetter.pointX;
        lastY = hasLetter.pointY;
        highlights.push(hasLetter);
      } else {
        $scope.found = false;
      }
    });
  }

});