I completely disagree. What sort of message are you sending him if you agree that the women in his life don't deserve anything for themselves, ever? That his future wife shouldn't spend a penny of her own salary on herself - everything should go towards her husband or her kids, and she comes at the bottom of the pile? It's hardly an all expenses paid trip to Dubai and doesn't sound like OP is having multiple holidays without him every single year. What's next - she shouldn't buy herself new clothes and should go around in rags in order for him to buy expensive trainers?
The two things are separate - £100 is a perfectly decent amount to spend on a 16 year old for a birthday, particularly from a parent on just over minimum wage. It doesn't make any difference that it was "only" £50 from his dad and £50 from OP and I don't get why posters are representing it that way - it would have been the same amount had they still been together.
I can see the point some posters are making that he might be conflating the amount spend with effort/fuss made of him. But whether that's relevant all depends on what you would have done if you hadn't gone away.
If your arrangement with his dad would mean that you wouldn't have seen him on his birthday regardless of whether you live in the next street or were in a different country, then he is being completely U. If, had you not been away, you probably would have seen him in the morning or evening, and then gone out the next day, maybe it's slightly more understandable - but either way the real person who he should be blaming if he had an underwhelming celebration was his dad, the parent he was actually with! It's completely illogical that he's happy staying with him but punishing you, when he also "only" gave him £50 (and couldn't even be bothered to organise that himself!)
You've already said you would have celebrated as soon as you were home - this is completely normal and lots of kids do the same, e.g. if their parents work long hours or the child has a commitment or wants to do something with their friends on the actual birthday - completely fine to delay 'family' celebrations until the weekend, so if he was upset at what he sees as a lack of effort, he's brought that upon himself!
I'd maybe send him a message offering to give him the additional £50 you were planning on spending on a meal out anyway, on the condition he comes home and has a proper conversation with you. It's been so long now it would be silly to have such a delayed meal out, and it's money you had earmarked for him anyway. Then have a chat explaining that if that is how he feels, then that's fine, but now he's getting older he has a responsibility to tell people if they have upset him and why, in a constructive manner. Insulting people and calling them stingy when presumably he knows that you work hard to clothe, feed, and house him, is hurtful and isn't ever going to get someone on side!