"\1" means the first opened parenthesis. You need to use "\2".
$ perl -e '$_="aaabbccccddeee"; print $1,$/ while /((.)\2*)/g'
# ^^
# ||
# |+--- \2
# |
# \1
aaa
bb
cccc
dd
eee
Or, if you want an array as a result,
push @array, $1 while /((.)\2*)/g;
Update
Notice that you can't just assign the outcome of the regex to an array, because you'd get redundant results (both $1 and $2 for each match).
# THIS IS WRONG
@array = $_ =~ /((.)\2*)/g;
print join ", " , map {"<$_>"} @array;
__END__
<aaa>, <a>, <bb>, <b>, <cccc>, <c>, <dd>, <d>, <eee>, <e>
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