No, the Strength reduction isn't increased.
Critical hits say the following:
When you score a critical hit, you get to roll extra dice for the attack’s damage against the target. Roll all of the attack’s damage dice twice and add them together. Then add any relevant modifiers as normal. To speed up play, you can roll all the damage dice at once.
For example, if you score a critical hit with a dagger, roll 2d4 for the damage, rather than 1d4, and then add your relevant ability modifier. If the attack involves other damage dice, such as from the rogue’s Sneak Attack feature, you roll those dice twice as well.
And the Shadow's Strength Drain ability reads as follows:
Strength Drain. Melee Weapon Attack: +4 to hit, reach 5ft., one creature. Hit: 9 (2d6 + 2) necrotic damage, and the target's Strength score is reduced by 1d4.
Note the key phrasing here: "the target's Strength score is reduced by 1d4", not, e.g., "the target takes 1d4 Strength damage". There's no concept of ability damage in 5e. The Strength reduction isn't any kind of damage, so it isn't multiplied on a critical hit.