$myArray[$row] is a reference to an array, you seem to be adding it to the actual numbers in the columns. That's why the values are so high. You can simplify the algorithm by iterating over the values rather than indices:

#!/usr/bin/perl
use warnings;
use strict;
use feature qw{ say };

my @content = (<DATA>);

my $no_of_seq = scalar(@content);

my @myArray;
for my $row (@content) {
    my @columns = split ' ', $row;
    push @myArray, \@columns;
}

say join "\t", $myArray[0][0], 'sum';
my $width = $#{ $myArray[0] };
for (my $row = 1; $row < $no_of_seq; $row++){
    print $myArray[$row][0], "\t";
    my $sum = 0;
    for my $col (@{ $myArray[$row] }[1 .. $width]) {
        $sum += $col;
    }
    say $sum;
}

__DATA__
GeneID    Tp1    Tp2    Tp3
ALA1    10    12    11
THR8    57    99    12
HUA4    100    177    199
ABA5    2    5    10
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Update: But, to compute a sum of a row, you don't need the other rows, so you can process the file line by line, no need to store it into an array. List::Util already exports the sum sub, no need to compute it yourself.

#!/usr/bin/perl
use warnings;
use strict;
use feature qw{ say };

use List::Util qw{ sum };

<DATA>;  # ignore the first line;
say "GeneID\tSum";

while (<DATA>) {
    my @cols = split ' ';
    my $sum = sum(@cols[1 .. $#cols]);
    say join "\t", $cols[0], $sum;
}
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