We have to decide if there is a selection or not:
TextEditor.TextArea.SelectionChanged += (sender, args) =>
{
  if (string.IsNullOrWhiteSpace(TextEditor.SelectedText))
  {
    foreach (var markSameWord in TextEditor.TextArea.TextView.LineTransformers.OfType<MarkSameWord>().ToList())
    {
      TextEditor.TextArea.TextView.LineTransformers.Remove(markSameWord);
    }
  }
  else
  {
    TextEditor.TextArea.TextView.LineTransformers.Add(new MarkSameWord(TextEditor.SelectedText));
  }
};
And here is the DocumentColorizingTransformer class:
public class MarkSameWord : DocumentColorizingTransformer
{
  private readonly string _selectedText;
  public MarkSameWord(string selectedText)
  {
    _selectedText = selectedText;
  }
  protected override void ColorizeLine(DocumentLine line)
  {
    if (string.IsNullOrEmpty(_selectedText))
    {
      return;
    }
    int lineStartOffset = line.Offset;
    string text = CurrentContext.Document.GetText(line);
    int start = 0;
    int index;
    while ((index = text.IndexOf(_selectedText, start, StringComparison.Ordinal)) >= 0)
    {
      ChangeLinePart(
        lineStartOffset + index, // startOffset
        lineStartOffset + index + _selectedText.Length, // endOffset
        element => element.TextRunProperties.SetBackgroundBrush(Brushes.LightSkyBlue));
      start = index + 1; // search for next occurrence
    }
  }
}