Nim

Solution: sort numbers using custom rules and compare if sorted == original. Part 2 is trivial.
Runtime for both parts: 1.05 ms

proc parseRules(input: string): Table[int, seq[int]] =
  for line in input.splitLines():
    let pair = line.split('|')
    let (a, b) = (pair[0].parseInt, pair[1].parseInt)
    discard result.hasKeyOrPut(a, newSeq[int]())
    result[a].add b

proc solve(input: string): AOCSolution[int, int] =
  let chunks = input.split("\n\n")
  let later = parseRules(chunks[0])
  for line in chunks[1].splitLines():
    let numbers = line.split(',').map(parseInt)
    let sorted = numbers.sorted(cmp =
      proc(a,b: int): int =
        if a in later and b in later[a]: -1
        elif b in later and a in later[b]: 1
        else: 0
    )
    if numbers == sorted:
      result.part1 += numbers[numbers.len div 2]
    else:
      result.part2 += sorted[sorted.len div 2]

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