"playful actions are not directed to something else." But it is a requisite of virtue that the agent in choosing should "direct his action to something else,"
I am a bit confused on how to interpret this. From looking at the link, the "Philosopher" he refers to is Plato, and the quote I am guessing, from the citations, is from Plato's ethics. Plato lists several virtues: courage, moderation, piety, and justice (Scavone 2023). I'd like to read the original by Plato before making real conclusions, but I believe the author's argument is appealing to both the virtues of moderation and piety. We've established already that among the differing medieval attitudes around games, one of the conclusions was moderation was key, such as this passage selected from the textbook, which was originally by John Salisbury, "'There are, however, times when, viewed from a certain aspect, games of chance are permissible. For example, if without evil consequences they alleviate the strain of heavy responsibilities and if without harming character they introduce an agreeable period of relaxation. Liberty to do as one pleases is justified if moderation controls the act'" (Milliman, 587), and so it's easy to see how, say, dice games would contradict Plato's virtue of moderation from a more severe perspective, since they can become addictive and make a gambler of a person. There is also a contradiction to the virtue of piety that the author may be appealing to, that since a person should "direct his action to something else" he means, potentially, that games distract a person from both their other responsibilities (both religion and justice if you were to look at it under the lens of Plato's virtues) and from the worship of God, not because a person should be spending every second of their time on these things, but because they have the capacity to steer a person the wrong way and tempt them away from keeping to the virtues.
I've left a link to the article I looked at here, it is by Daniel C. Scavone.