I agree with your thought that Ra is communicating a correspondence between play and pleasure in those words.
When attempting to grasp the meaning of existence through The Law of One, the expression of free will is the paramount element, so we must remember that play and pleasure must stem from that root. Ultimately, something pushes each of us to express our free will in an polarized or unpolarized manner. In the context of the Law of One, we see this thought reflected in the concept of desire.
Ra speaks a few times on desire which appear relevant:
The proper role of the entity is, in this density, to experience all things desired, to then analyze, understand, and accept these experiences, distilling from them the love/light within them. 18.5
…[the Veil] offers an opportunity for a desire to grow within the mind complex. 86.18
In the magical personality desire, will, and polarity are the keys. 73.11
That being said, Ra did not directly comment on the nature of desire, at least to my knowledge. The consciously-channeled sources more directly addressed desire, which I briefly explored in a previous post. In essence, whereas will causes doing, desire causes the origination of what we do. With Ra’s insightful quote on the magical personality, will and desire appear to be complementary elements. (If someone here is aware of how desire and will emerge from the archetypal mind, sharing such knowledge would be most appreciated.)
With this initial ground established, let us now broach how will and desire drives play and pleasure. As you helpfully point out, when one plays, one experiences pleasure. However, is that statement always true? Can one feel pleasure without play? Furthermore, can one play without feeling pleasure?
The first question—if pleasure may be experienced independent of play–is relatively simple to answer. As a simple example, a simple kind word from a stranger may brighten your whole day. You may or may not be at play when this happens; you may be sitting in a coffee shop, walking down the street, riding the subway, or be anywhere else people are. As such, we answer with resounding yes: pleasure may be experienced independent of play.
The answer to the second question–if “pleasureless play” exists–is more interesting. When pursued in its purest form, play does not have at its core a constructive element. Consider children playing catch with a ball in a circle. One may argue that such an activity will improve the children’s motor skills, which may be true. That said, the number of children who play catch are almost certainly not consciously working to improve their motor skills at a specific activity, for one who does then starts to become an athlete. Furthermore, children may be compelled to play catch by instruction from a schoolteacher. Some children may wish to leave and pursue other activities, but the teacher requires them to continue playing catch. These children could not be said to be engaging in play because the participation is forced, the fun element is mandatory. As such, I argue play must include some element of pleasure, and therefore “pleasureless play” cannot exist.
Let us now return back to the previous line of reasoning, attempting looking at how will and desire relate to play and pleasure. In its essential form, play is something we choose to do. To play is, at its core, to express our will. What makes us want to play is an internal desire to experience pleasure. Just as will and desire go hand-in-hand, so do play and pleasure. Will and play each have a masculine quality, whereas desire and pleasure have a counterbalancing feminine quality.
Given that will and desire are explicitly mentioned by Ra as important to the magical personality while play and pleasure are not, I am inclined to adopt the position that play/pleasure are one specific way to express our will/desire in our life, to become the Creator.