shot in the gut

It is likely that Squier, while in pain, can move himself enough, especially with his arms, to move closer to Gabby and/or to fall upon her.

If Squier is shot and quickly dies after it is mostly likely due to internal bleeding in a vital organ, such as the liver, stomach, or, especially, the spleen. If you get shot in or through the spleen, you will likely die soon after. Moving around, which might help push the bullet further around in the organ, might even speed up the dying process as it will cause more bleeding.

Squier is able to move during this painful process because even though he anticipated Duke shooting him, human response to wounds like this still require the brain to fully process what is happening to the body.  In other words, the brain won't immediately stop the body from moving and responding to a fatal wound, so especially right after getting shot, Squier would be able to move himself.

For the sake of following the logic of the scene, it's probably best to assume that Squier does get shot in a vital organ like spleen because he dies within three minutes.

(I would like to thank my mother, the nurse, for help with this one.)