This sounds an awful lot like "A Dry, Quiet War" (1996) by Tony Daniel, which has previously been asked about and answered here (where it was accepted) and here (where it was not, but there are no other answers offered).
The story can be read in its entirety online at InfinityPlus, so it should be easy enough to check. It does indeed feature a soldier of a future war in an altercation with another veteran over a woman, with multi-dimensional combat:
"Colonel Bone," he began. "If I'd knowed it was you"
"Too late for that."
"It's never too late, that's what you taught us all when you turned
that offensive around out on the Husk and gave the Chaos the what-for.
I'll just be going. I'll take the gang with me. It's to no purpose,
our staying now."
"You knew enough yesterday enough to leave." I felt the rage, the
old rage that was to be, once again. "Why did you do that to her?" I
asked. "Why did you "
And then I looked into his eyes and saw it there. The quiet desire
beaten down by synthesized emotions, but now triumphant, sadly
triumphant. The desire to finally, finally die. Marek was not the
unthinking brute I'd taken him for after all. Too bad for him.
I took a step toward Marek. His instincts made him reach down, go for
the trunch. But it was a useless weapon on me. I don't have myelin
sheaths on my nerves. I don't have nerves anymore; I have wiring.
Marek realized this was so almost instantly. He dropped the trunch,
then turned and ran. I caught him. He tried to fight, but there was
never any question of him beating me. That would be absurd. I'm
Colonel Bone of the Skyfalling 8th. I kill so that there might be
life. Nobody beats me. It is my fate, and yours, too.
I caught him by the shoulder, and I looped my other arm around his
neck and reined him to me not enough to snap anything. Just enough
to calm him down. He was strong, but had no finesse.
Like I said, glims are hard to kill. They're the same as snails in
shells in a way, and the trick is to draw them out way out. Which
is what I did with Marek. As I held him physically, I caught hold of
him, all of him, over there, in the place I can't tell you about,
can't describe. The way you do this is by holding a glim still and
causing him great suffering, so that they can't withdraw into the deep
places. That's what vampire stakes and Roman crosses are all about.
And like I told Bex, glims are bad ones, all right. Bad, but not the
worse. I am the worse.
and, due to this, he must return to fight the war again:
Irrevocably gone from this time line, and that was what mattered.
Keeping this possible future uncertain, balanced on the fulcrum of
chaos and necessity. Keeping it free, so that I could go back and do
my work...
I went to the living room, to the shroud-covered furniture. I sat down
in what had been my father's chair. I sipped a cup of my father's best
barley malt whisky. I sat, and as the suns of Ferro rose in the hard
iron sky, I faded into the distant, dying future.
