You have to change your code like,

print "file1 ="; 
$file1=<stdin>;
print "file2 =" ;
$file2=<stdin>;
@ARGV = ("$file1", "$file2") ;
chomp($remove = <stdin>);
chomp($replace = <stdin>);
while(defined($line=<>)){
 $line =~ s/$remove/$replace/g;
 print "$line"; }
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When your code seems not giving the expected result, you can use the perl debugger to find out issue.
I debugged the code, after made the change from {} to ()

main::(./dynamic_file.pl:22):   print "file1 =";
  DB<1> n
main::(./dynamic_file.pl:23):   $file1=<stdin>;
  DB<1> n
file1 =file1
main::(./dynamic_file.pl:24):   print "file2 =" ;
  DB<1> n
main::(./dynamic_file.pl:25):   $file2=<stdin>;
  DB<1> n
file2 =file2
main::(./dynamic_file.pl:26):   @ARGV = ("$file1", "$file2") ;
  DB<1> n
main::(./dynamic_file.pl:27):   chomp($remove = <stdin>);
  DB<1> p @ARGV
file1
file2
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