Causal claim for age would be inappropriate in this case
The problem with claiming causality in your exam question design can be boiled down to one simple fact: aging was not a treatment, age was not manipulated at all. The main reason to do controlled studies is precisely because, due to the manipulation and control over the variables of interest, you can say that the change in one variable causes the change in the outcome (under extremely specific experimental conditions and with a boat-load of other assumptions like random assignment and that the experimenter didn't screw up something in the execution details, which I casually gloss over here).
But that's not what the exam design describes - it simply has two groups of participants, with one specific fact that differs them known (their age); but you have no way of knowing any of the other ways the group differs. Due to the lack of control, you cannot know whether it was the difference in age that caused the change in outcome, or if it is because the reason 40-year olds join a study is because they need the money while 20-year olds were students who were participating for class credit and so had different motivations - or any one of a thousand other possible natural differences in your groups.
Now, the technical terminology for these sorts of things varies by field. Common terms for things like participant age and gender are "participant attribute", "extraneous variable", "attribute independent variable", etc. Ultimately you end up with something that is not a "true experiment" or a "true controlled experiment", because the thing you want to make a claim about - like age - wasn't really in your control to change, so the most you can hope for without far more advanced methods (like causal inference, additional conditions, longitudinal data, etc.) is to claim there is a correlation.
This also happens to be one of the reasons why experiments in social science, and understanding hard-to-control attributes of people, is so tricky in practice - people differ in lots of ways, and when you can't change the things you want to learn about, you tend to need more complex experimental and inferential techniques or a different strategy entirely.
How could you change the design to make a causal claim?
Imagine a hypothetical scenario like this: Group A and B are both made up of participants who are 20 years old.
You have Group A play the dictatorship game as usual.
For Group B, you take out a Magical Aging Ray of Science (or perhaps by having a Ghost treat them with horrifying visage), which you have carefully tuned to aging all the participants in Group B so that they are now 40 years old, but otherwise leaving them unchanged, and then have them play the dictator game just as Group A did.
For extra rigor you could get a Group C of naturally-aged 40-year olds to confirm the synthetic aging is comparable to natural aging, but lets keep things simple and say we know that artificial aging is just like the real thing based on "prior work".
Now, if Group B keeps more money than Group A, you can claim that the experiment indicates that aging causes people to keep more of the money. Of course there are still approximately a thousand reasons why your claim could turn out to be wrong, but your experiment at least has a valid causal interpretation.