Yes, Express Air is still operating, but (like other smaller Indonesian domestic airlines) they do not have online booking.
I also get the same Norton warning message from the Express Air website, but I ignore it and have no problem. The EA website works better with Internet Explorer than other web browsers; for example, the flight schedule only loads up properly in IE.
Here is the schedule for flights between Jayapura and Sorong:
As you can see, there are daily direct flights.
You can read a more general post about Express Air flights to Sorong here:
One drawback is that Express Air only accepts bookings up to 30 days in advance.
If you do want to book an Express Air flight, you can send an enquiry here: