g is not a valid modifier for qr (see the description of qr under "Regexp Quote-Like Operators" in perldoc perlop for a list of valid modifiers). You can do what you want this way:

my $line = 'marker <this> <that> <other>';
my $rex = qr/(?:^marker\s|\G)<(.*?)>(?: |$)/;
my @matches = ($line =~ /$rex/g);
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