You actually did an excellent job but I have some few observations and suggestions

You just simply enter your Bitcointalk profile link and the system will:
I didn't notice the instructions correctly, I inserted my username and it displays error message. Then I realised it requires Profile link and not username
I had to go back and get my profile link for another trial. And it works fine this time.
Isn't it more easier to use username instead of profile link? I'm actually more convenient with username

Show a live countdown (days remaining)
Show a
live countdown. Since it displays only days remaining, it's not accurate to say it's a live countdown. It's still a countdown but live countdown usually update second by second. Shows days countdown (static countdown) is more appropriate in this case. Or you can update it to show live countdown by updating second by second if you prefer to use the live countdown.
Generate a downloadable Anniversary Share Card
I downloaded the card but it only carries Username and anniversary date.
If you share the card without any caption, then people will start wondering what anniversary you're actually celebrating. So I suggest you include "10th years anniversary on Bitcointalk" to the share card since this is about 10th year anniversary tracker.
It is just a fun way to see your forum milestone ahead of time. Appreciate long-term participation on Bitcointalk Forum and add a bit of excitement around anniversaries
Since it's a fun way to see your forum milestones ahead of time, it's not necessarily needed to be 10 years. Make the year optional for people to choose from as low as one year. 10 year is a actually a bit too long.
Someone already suggested a notification system. It would be close to meaningless tracking an event without a notification especially for some thing that is as long as 10 years. The notification can be through email or other means. You may make it optional thou but it's necessary.