That's quite easy. Just ask Perl to tell you what it sees:

Q:\>perl -w -MO=Deparse -e "s;;new;;old;;g"
Unquoted string "old" may clash with future reserved word at -e line 1
+.
Unquoted string "g" may clash with future reserved word at -e line 1.
Useless use of a constant in void context at -e line 1.
Useless use of a constant in void context at -e line 1.
BEGIN { $^W = 1; }
s//new/;
'???';
'???';
-e syntax OK
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So basically, your program is equivalent to $one =~ s//new/;, which replaces the first empty place in the string $one with new, which is what you see.

Also, this shows again why running with warnings enabled reveals many problematic spots in the code.