HN user
You don't owe them anything.
They don't show you the same level of trust that they expect from you. Nowhere close.
If it's important to you, and okay with your new company, give your current employer a little extra notice. But don;t feel obligated—only do it if it's important to you.
I work for a 30-employee company that only hits your first bullet point, but I wish it hit a lot more.
Someone where I work setup a similar app, only telling 3-4 people. Then, they built some really creepy/invasive stats into the service/page, too.
Just some advice: for each feature you add, make sure you consider how creepy/intrusive it is first. Nobody wants to be the person to object to something like this and, frankly, they shouldn't have to be.
A complete and total disregard for coworker's personal space and privacy.