He didn't allow for spaces between the two equals signs. Try this version:

my $re =  qr[<!--QBlastInfoBegin \s+
  RID \s* = \s* ([\d-]+) \s+
  RTOE \s* = \s* (\d+) \s+
QBlastInfoEnd  \s+
-->]x;
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As for the pluses, they are quantifiers and make the expression match one or more spaces (in this case). See perldoc perlre for more info.