The problem is I get a "Can't use string ("OUTPUT1") as a symbol ref while "strict refs" in use" error. Where have I gone wrong?

Others already told you what you're doing wrong, and I also concur with grep that you're making things overly complicated. I want to contribute, and here's how I'd do it:

#!/usr/bin/perl

use strict;
use warnings;

chomp(my $line=<>);
my @line=split /\t/, $line;

{
    my @fh=map {
        my $fname=sprintf 'output%02d.txt', $_;
        open my $fh, '>', $fname or
          die "Can't open `$fname': $!\n";
        $fh } 1..$#line;
    
    sub doline {
        my $one=shift;
        print { $fh[$_] } "$one\t$_[$_]\n" for 0..$#_;
    }
}
            
doline @line;
chomp, doline split /\t/ while <>;

__END__
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