First, I'm going to agree with you. Full out, no reservations.
Second, I'm going to explore the edges of that.
Whenever I had cool superhero character ideas, I built them in Champions (now Hero System) for literal decades after the last time I played. I enjoyed doing so. Can "play" only happen at the table, or can there be mini-games like character-creation/advancement that happen away from the table.
Another example of the same, I have more setting/campaign ideas then I will ever have a chance to run. I enjoy coming up with them and working on them. Is this also a "mini-game" that can be considered part of play?
Okay, how about another edge -- I'm mentoring a first time DM. I won't be at their play table, but I'm helping them come up with things and we're collaborating and I'm teaching and we're both having fun. Is that part of play? If it is, how about if I'm not mentoring, just the sounding board for a friendly DM? If that is, is enjoying making adventures for DMsGuild still play?
Again, I agree with your foundation, I'm just exploring if play can only happen "at the table".