The AAR track *does* have wiggle in it, and if viewed from the rear the missile can be seen to oscillate, and deviate from the direct path to some extent... when viewed from the side or zenith however the track seen in the video would appear almost straight, as is the impression given by the default views of the AAR.

(why I've never been very convinced of drastic reduction in range with low to moderate manoeuvre requirements ~ the missile is usually flying with some AOA and 'g' load to follow/recross the desired mean path... if a turn is required the corrections become single sided and the missile turns ~ but there may be less, or a similar overload compared to the straight path).