General Zaroff was in the army, but so was Rainsford.

Zaroff is fully aware that Rainsford was in the army.  Almost every man his age would have fought in World War I.  When Zaroff is explaining his views on the acceptable nature of killing whatever men he feels inferior, he seems to think that Rainsford having been a soldier would make him agree with his views.

He regarded Rainsford quizzically. "I refuse to believe that so modern and civilized a young man as you seem to be harbors romantic ideas about the value of human life. Surely your experiences in the war--"

"Did not make me condone cold-blooded murder," finished Rainsford stiffly.

Rainsford became an experienced hunter, and even wrote books on the subject.  This is one of the reasons that Zaroff knows so much about him.  He respects Rainsford’s abilities.  He knows that between his service in the war and his hunting skills he will be a very good competitor.  Zaroff can’t wait to hunt him.

During the hunt, Rainsford does use his war experience to aid him in evading Zaroff.  The combination of hunting skills and war experience indeed makes him a formidable foe.

Rainsford had dug himself in in France when a second's delay meant death. That had been a placid pastime compared to his digging now. The pit grew deeper; when it was above his shoulders, he climbed out and from some hard saplings cut stakes and sharpened them to a fine point.

Zaroff’s experience in the army was likely different than Rainsford’s.  Rainsford was clearly in the thick of it.  Zaroff, on the other hand, joined the Russian army as an officer because that was what was expected of a wealthy young man.

“…I went into the army--it was expected of noblemen's sons--and for a time commanded a division of Cossack cavalry, but my real interest was always the hunt. I have hunted every kind of game in every land. It would be impossible for me to tell you how many animals I have killed."

Zaroff considers his entire life one long hunt.  To him, the fact that he ended up on the wrong side of the Russian “debacle” known as the Russian Revolution meant little.  He just went off to create his own little island kill zone.  Clearly he had plenty of money left.