Using the code you posted and the data above I get the answer:

2429

This code also gives the same answer:

#!/usr/bin/perl
use strict;
use warnings;


#  2429


my @row = do {
    open my $lines, '<', 'input8.txt';
    map [ /\d/g ], <$lines>;
    };

my $visible = 198;

for my $current ( 0 .. $#row ) {
    if ( $current > 0 && $current < 98 ) {
        $visible += 2;
COUNT:
        for my $i ( 1 .. 97 ) {
            my $counter = 1;
            while ( $row[ $current ][ $i - $counter ] < $row[ $current
+ ][ $i ] ) {
                if ( ++$counter == $i ) {
                    ++$visible;
                    next COUNT;
                    }
                }
            while ( $row[ $current ][ $i + $counter ] < $row[ $current
+ ][ $i ] ) {
                if ( ++$counter == $i ) {
                    ++$visible;
                    next COUNT;
                    }
                }
            while ( $row[ $current - $counter ][ $i ] < $row[ $current
+ ][ $i ] ) {
                if ( ++$counter == $current ) {
                    ++$visible;
                    next COUNT;
                    }
                }
            while ( $row[ $current + $counter ][ $i ] < $row[ $current
+ ][ $i ] ) {
                if ( ++$counter == $current ) {
                    ++$visible;
                    next COUNT;
                    }
                }
            }
        }
    }

print "$visible\n";
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