Dart solution

Quite straightforward, though there's a sneaky trap in the test data for those of us who don't read the rules carefully enough.

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parseLine(String s) {
  var game = s.split(': ');
  var num = int.parse(game.first.split(' ').last);
  var rounds = game.last.split('; ');
  var cubes = [
    for (var (e) in rounds)
      {
        for (var ee in e.split(', '))
          ee.split(' ').last: int.parse(ee.split(' ').first)
      }
  ];
  return MapEntry(num, cubes);
}

/// collects the max of the counts from both maps.
Map merge2(Map a, Map b) => {
      for (var k in {...a.keys, ...b.keys}) k: max(a[k] ?? 0, b[k] ?? 0)
    };

var limit = {"red": 12, "green": 13, "blue": 14};

bool isGood(Map test) =>
    limit.entries.every((e) => (test[e.key] ?? 0) <= e.value);

part1(List lines) => lines
    .map(parseLine)
    .where((e) => e.value.every(isGood))
    .map((e) => e.key)
    .sum;

part2(List lines) => lines
    .map(parseLine)
    .map((e) => e.value.reduce(merge2))
    .map((e) => e.values.reduce((s, t) => s * t))
    .sum;