Just count the spaces and add 1:

    // No need to count markup.
    $text        = trim( strip_tags( get_the_content() ) );
    $word_number = substr_count( $text, ' ' ) + 1;

Another way, taking the old American double space tradition into account:

    $word_number = preg_match_all( '~\s+~', $text, $m ) + 1;