This effects is Directional Blur. It seems that the amount and direction of blur is driven by an expression (maybe the random expression).
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Looks like simple scaling of separated x & y parameters (maybe using wiggle)
Also a simple animated cross blur maybe two cross blurs, one for the x scale and one for the y scale.
Maybe the blur amounts were pick whipped to the scale's wiggle expressions & re-interpolated to usable values.
In other words if the text is scaling in the range of 100 to 120 but the blur effect works in the value range of 1 to 10
then you'll have to divide the values being passed to the blur amounts by around 20.
You could also look into "glitch effects". It kind of looks like that was what whoever made that was trying to create.
But the effect can be taken much further.
I've tested 3 options and it looks very similar.
The first one with Directional Blur effect. Adding a random(360) expression to the Direction parameter and another random(120) expression to the Blur Amount. 360 and 120 values can be changed for any other value
The second one involves two Gaussian Blur effects for controling only x&y blur direction. Put the random expressions in the blur amount for the 2 effects.
The third effects, as Gutter-Fish said is the Cross Blur Effect, but this one maintains the original element very sharp. Anyway is a valid option too.