The code

map {$x += $$_[0]; $y += $$_[1];} @{$r{$k};};

is better written as:

for (@{ $r{$k} })   { $x += $_->[0]; $y += $_->[1]; }

(Using map statement in void context in lieu of for is confusing.)

The dereferences are used because the structure is populated with array references. In other words, you have a hash of arrays (HoA). See perldata, perldsc.

Specifically, look at the matching statements:

push @{ $r{ ... } }, [ ... ];
...
for (@{ $r{ ... } })  { ... $_->[...] }
[download]

The first populates the HoA with necessary data. The second one uses this data further down. Why HoA, why the need for array [ constructors ] and dereferences? Because one scalar was not enough. The original programmer needed to track two values and used the small arrays as tuples.