Two people of equal builds will burn the same amount of calories doing the same activity regardless of age. A younger person will have more metabolic activity and therefore burn more calories DURING the activity, but a younger person will still burn the same amount of calories FROM the activity.
If you noticed, there are two caveats to that conclusion. The first is that my conclusion requires the two hypothetical people to be of the same build, which isn’t common even among people in the same age group, there is a ton of diversity among people. The second is that the two people are doing the same activity, which might sound cut and dry, but it isn’t. Two people could go for a mile walk and one could work harder simply because their legs are shorter. Two people could lift a 10 lb dumbbell and one work harder because they have less muscle mass.
Age itself isn’t a factor for the calories burned from an activity, but it can effect other things that are factors (height, strength, stamina, etc).