I have been in a similar situation, but the pressure to reciprocate has come from inside me not from other parents. Similar in that there are 3 households, and one (not mine) has great play equipment.
I would say that keeping things balanced as to whose house the kid gang plays at is important. They are clearly more vigilant in their parenting style, which is fine at their house. Of course they don’t get to dictate your style at your house. But other than the 10yo, it would be unusual around my circles not to supervise/direct a bit when they play at my house. And also common to make a point of inviting the other kids around for a more guided activity, to keep the balance.
I’d set up a few ‘loose’ activities in nice weather, or make a few suggestions, and def an more directed activity or game for indoors weather. Even if it’s just setting up a speaker and playlist for them to do crazy dancing to. Or pulling out the popcorn machine with different bowls of flavourings. Then I’d leave them to it, with clear instructions for cleaning up, etc.
In my view, it’s very unlikely that 3 households will all share the ‘free play is the way’ ideology. So you do need to keep an eye on the balance of ‘whose house’. If you don’t err on the side of inviting/offering you almost certainly will find that you’ve built resentment in others. By the time they let you know it, it’s a problem. Frankly, I’ll do almost anything to avoid those conversations and hurt feelings (and having to try and keep my kid home!).
I’ve had to put myself out a few times, arranging play dates at mine, just to be fair. I hate the mess, the noise and the constant demands for attention. But it’s the price of having my kid ‘out of my hair’ at other times. I splash a little cash with craft kits, sport equipment (hula hoops, etc) so that the neighbour kids report back they had fun. Often they go home with a skill or a craft. I find that one play date like that buys me about 3-4 longer ‘free play’ play dates at theirs. Extra points if you feed them, and send something back for the parents
. It’s my insurance policy, and it works.
I won’t take the kid gang out, other than the local park, but in order to stick with that policy (which is entirely for my own convenience) I know I have to make up for it in other ways.
The idea that the kids just all entertain themselves like in the 1970’s, or that all the parents will have the same ‘live and let live’ attitude is just a bit pie-in-the-sky for me. Your kid (like mine) can play alone or without set activities, but is choosing to hang with the gang. So you have to play by gang rules, I’m afraid, or prevent yours from going over.