time_output.rb

command = ARGV
start = Process.clock_gettime Process::CLOCK_MONOTONIC, :millisecond

IO.popen(command, err: [:child, :out]) do |io|
  while line = io.gets
    now = Process.clock_gettime Process::CLOCK_MONOTONIC, :millisecond
    puts "[#{"%5d" % (now - start)}] #{line}"
  end
end

Example:

$ ruby time_output.rb ruby -e 'STDOUT.sync = true; sleep 0.1; STDOUT.puts "out"; sleep 0.1; STDERR.puts "err"'
[  134] out
[  234] err

Note the needed STDOUT.sync = true (or STDOUT.flush), otherwise STDOUT might be block-buffered since it's not a TTY (but a pipe).
This is currently not needed on TruffleRuby as there is no write buffering (only read buffering).