I think this is a very interesting topic as my livelihood is conducting the fitness evaluations for the CF. Both the guys in the video and BDave present excellent points. Although the video is referring to US military fitness evaluations, it still holds true when we consider the EXPRES.
If you look at most military occupations, being able to run 20 meters back and forth, squeeze a handgrip, rep out 7-19 push-ups, and reps out 12-19 sit-ups does reflect specific job requirements.
The PT tests elements that the staff in the video mention would definitely be good for Combat Arms soldiers. (They actually justified with their comments the value of the BFT for army personnel) However, the mentioned tests in the video may not be that relevant for Naval personnel or many Air Force jobs. As BDave said, they also don't reflect some army jobs like cook or clerk. That does not matter because the DAOD 5023-0 Universality of Service state that all soldiers regardless of trades are soldiers first and must meet the minimum operational standards for basic soldiering skills.
For this reason the CF conducted a massive study to determine physical tasks that are common or could potentially be common to all serving military personnel. The result of that study lead to the development of the Common Military Task Fitness Evaluation (or 5 Common Tasks). (For specific details on it: http://canadianmilitaryandefence.blogspot.com/2010/09/common-military-task-fitness-evaluation.html) This test involves a sea evacuation, land evacuation, sandbag carry, trench dig, and high-low crawl. This test currently reflects the Minimum Physical Fitness Standard (MPFS) for all CF members.
As everyone is aware, members do not conduct the 5 Common Task test each year. So your thinking why aren't soldiers tested in it if it is relevant? Well the equipment required for the test is expensive, cumbersome, and requires a lot of space to store and use during a test. For that reason it is only available at a select few bases. Also, the evaluation process takes a very long time to do. If you go to the above link, you will notice that the test is 4 day process.
Since physical fitness is a BONA FIDE OCCUPATIONAL REQUIREMENT (A legal term meaning human life is potentially at risk for these requirements aren't met) of all soldiers, they needed to find a more feasible testing protocol. The researchers involved in the 5 common tasks test decided to test people in it as well as test them with the EXPRES Protocols. After comparing results they found that there was a strong correlation between the EXPRES results and the 5 common task results with individual members. So it was determined that the EXPRES Test is a good indicator of ones ability to conduct the 5 common tasks, and therefore, the EXPRES is the CF standard because it is economical and better suited for testing larger numbers.
CF members are able to conduct the 5 common task test, only after 2 consecutive failures on the EXPRES, as long a the obtain CO approval.
I hope this gives people some insight on the testing process.