I've not read the whole thread.
I get that you feel that committing a few of the approximately 730 hours in a month to share a takeaway with extended family isn't much to ask of your son (in addition to the 10+ birthdays which he's already coming back for).
But your son doesn't have 730 free hours in a month. He's got relatively small amounts of free time on the days when he's working, and more on the days he's not working. He's establishing a home, and life, with his girlfriend. It is entirely reasonable that he and his girlfriend consider how they want to prioritise spend their precious free time. They are entitled to spend it how they choose, regardless of your views on how frequently they should turn up for a takeaway with the extended family.
If I'd have faced the expectation of spending one in every four Friday evenings with my parents and extended family to have a takeaway, when I was young, working full time establishing a career and dating / coupling up, on top of hosting my parents at least once a month (is that during precious weekend time, or do you pop by for an hour or so on a mid-week evening that's convenient to them?), I'd have been setting firm boundaries, and perhaps also taking up a new hobby which just so happened to occupy every Friday evening. I certainly wouldn't have imposed the expectation on my partner to spend 25% of Friday nights eating takeaway with their extended family-in-law.
Do you think your son enjoys coming to eat takeaway with you all? If not, do think it's reasonable to expect him to spend 25% of his Friday nights doing something he doesn't want to, out of a sense of obligation?
It seems to me that you have rather unreasonable expectations of how your son should choose to spend his limited free time.