There's no reason for it to. Going back to the FMS LEGS page you can see the constraints are 4600A, 3700A, etc. This reflects the altitudes on the chart being safe minimums, one is not expected to "dive-and-drive" anymore. You can see the TOD is just ahead of SILEX, that's where the 3 degree FMS glide path (not slope!) from the runway intercepts the current altitude (4600 feet). After approach was engaged and it switched to LOC guidance it was waiting to intercept the glide slope (GS was armed), you didn't have to do anything other than wait.
In the video you're in PPOS map mode, you're only going to see ghost needles in ROSE mode.
Seemed fine on capture? If you're referring to later in the approach this all comes down to the right engine going way up in N1 (multiple times) and hence a huge yaw moment being present, which the autopilot tried admirably to counteract, but there's only so much it can do. (Maybe there's some wild rudder input from the noisy hardware too.) Also appears that the rudder and aileron trim aren't centered. I wouldn't be surprised in the low FPS also came into play with the flight control laws and physics going into time dilation.