How to ‘burn’ a subtitle track onto an mp4 video file

First run ffmpeg -i file.mp4 to see which streams exists in your file. You should see something like this:

Stream #0.0: Video: mpeg4, yuv420p, 720x304 [PAR 1:1 DAR 45:19], 23.98 tbr, 23.98 tbn, 23.98 tbc
Stream #0.1: Audio: ac3, 48000 Hz, 5.1, s16, 384 kb/s
Stream #0.2: Audio: ac3, 48000 Hz, 5.1, s16, 384 kb/s

Then run ffmpeg -i file.mp4 -map 0:0 -map 0:2 -acodec copy -vcodec copy new_file.mp4 to copy video stream and 2nd audio stream to new_file.mp4.

This is very similar to @goldilock's approach but, IMO, simpler and can deal with empty lines in the file and replaces | with a line break :

#!/usr/bin/env perl
my ($time, $text, $next_time, $next_text);
my ($c,$i)=0;
while (<>) {
    ## skip bad lines
    next unless /^\s*([:\d]+)\s*:(.+)/;
    ## If this is the first line. I could have used $. but this is
    ## safer in case the file contains an empty line at the beginning.
    if ($c == 0) {
      $time=$1; 
      $text=$2;
      $c++;
    }
    else {
      ## This is the counter for the subtitle index
      $i++;
      ## Save the current values
      $next_time=$1; 
      $next_text=$2;     
      ## I am assuming that the | should be interpreted
      ## as a newline, remove this if I'm wrong.
      $text=~s/\|/\n/g;     
      ## Print the previous subttitle
      print "$i\n$time,100 --> $next_time,000\n$text\n\n";        
      ## Save the current one for the next line
      $time=$next_time; $text=$next_text;
    }
}     
## Print the last subtitle. It will be dislayed for a minute
## 'cause I'm lazy.
$i++;
$time=~/(\d+:)(\d+)(:\d+)/;
my $newtime=$1 . (sprintf "%02d", $2+1) . $3;
print "$i\n$time,100 --> $newtime,000\n$text\n\n";    

Save the script as a file and make it executable, then run:

./script.pl subfile > good_subs.srt

The output I get on your sample was:

1
00:00:44,100 --> 00:01:01,000
" Myślę, więc jestem".
Kartezjusz, 1596-1650

2
00:01:01,100 --> 00:01:06,000
Trzynaste Pietro

3
00:01:06,100 --> 00:01:10,000
Podobno niewiedza uszczęśliwia.

4
00:01:10,100 --> 00:01:13,000
Po raz pierwszy w życiu
zgadzam się z tym.

5
00:01:13,100 --> 00:01:15,000
Wolałbym...

6
00:01:15,100 --> 00:01:19,000
nigdy nie odkryć
tej straszliwej prawdy.

7
00:01:19,100 --> 00:02:19,000
Teraz już wiem...