Some ideas from me to start:
Virtual horse racing nights
Kahoot pub quiz. You host a Zoom call, the host shares their screen and players use their phones to submit their answers to each question. After each question a leaderboard is displayed. This really is great fun!
Cameo offer recorded video messages from celebrities (for payment, although some are quite reasonably priced). You message the celebrity with details of the special occasion and they reply with a message for the birthday boy or girl.
Hang doughnuts from the washing line and have a race to see who can eat theirs first with no hands.
Pinata
Would love to hear any other ideas. We have a birthday boy in the house and I'm racking my brains for ways to make his day special. He's a teenager so would happily spend the day on his room on the Xbox, although that doesn't have quite the "special" factor I'm aiming for!