I abruptly shifted to anime with the jumping frame, but it worked, and the fact that this seemed tactically odd in what the opening told me was a well-written story made sense when we found out what was going on. Nice touch.
I have a few suggestions and other comments below. Do as thou wilt shall be the whole of the law--in this case.
The other had Sergeants strips going down his sleeve...
You may want to use 'stripes'.
I'm wary of the cigar-smoking cool-as-ice sergeant, who could too easily turn into a cliche, but I trust you. Although extremely rare, there are people like that out there.
Cole swung the barrel around to face the rear of the truck, he racked the large charging handle...
...rear of the truck. He racked the...
..Jump Thrusters fired again, combined with...
...jump thrusters fired again. Combined with...
...some poor buck private, but Cole...
some poor buck private. Cole...
You may want to use 'buck sergeant'. There is such a thing as a buck private but I think it may be a more rarely-used term, less familiar to most readers.
Ensign Pelait Cerchenkov of the Terran Transit Marines was fighting a losing battle. He had been on duty for almost eight hours and was about to fall asleep at his station.
Yes! This is a great example of the reality of military life.
...but he continued anyways...
But he continued anyway,
Mr. Cerchenkov
Overall, you may good use of rich visual language to create a cinematic feel. It feels like you've thought about your characters. I'm looking forward to more of this!
Oh, and feel free to tell me to buzz off, and I'll leave out this sort of editorial business in future feedback.

