Why do the engineers need to be on board during testing?
More and more data is collected in flight testing of aircraft. While 50 years ago they might have only designed for a small number of scenarios, the advances in computing allow them to design modern aircraft for thousands of scenarios. Modern certification standards include more and more requirements, which include flight testing for many of these requirements.

While some information is sent to the ground (like in this video), other information may not be. Airplanes in flight test have sensors for temperature, pressure, stress, and many other parameters located throughout the plane. These generate a lot of data, more than may be practical to send on a live data link. There may be several reasons that the engineers would want to analyze a lot of information onboard.

Some of the tests need to have multiple parameters coordinated with the pilots. If they are flight testing stall, for instance, they need to be sure they have flight parameters are correct for that test. The engineers give the pilots guidance on getting the airplane into the right configuration. The engineers also verify that the the information they collect is sufficient for the needs of the test. It's much more expensive to come back and realize they didn't get what they needed and must go back up to re-run the test.

Some of the data is also critical for safety. One subject of the tests is flutter. Flutter conditions can be very dangerous to the aircraft. The engineers help monitor the data and make sure that things don't get out of hand. If a data link were to be interrupted in a case like this, safety could be compromised.