[valexiev]

?awardYear and ?dateOfBirth are literals, so you don't need to take *Label of them (that's only useful for Qnnn nodes).

Below I use a blank node (since you don't need the URL of ?statement) to simplify the query, and calculate the age as a difference of the two years:

    SELECT ?awardYear ?age ?winnerLabel WHERE {
      SERVICE wikibase:label { bd:serviceParam wikibase:language "[AUTO_LANGUAGE],en". }
      ?winner p:P166 [ # award won
          ps:P166 wd:Q185667; # Turing award
          pq:P585 ?awardDate]; # point in time
        wdt:P569 ?birthDate.
      bind(year(?awardDate) as ?awardYear)
      bind(?awardYear-year(?birthDate) as ?age)
    }
    ORDER BY ?age