Interesting question! Williams's choice certainly isn't as obvious as, say, the military march for Darth Vader. Although I can't find a definitive statement from Williams himself, I think there is a clear analytic way to make sense of his choice.
There is a branch of music analysis called "topic theory." In short, topic theory looks at conventional musical signs that signify some kind of emotion or background. A group of trumpets quickly articulating arpeggios, for instance, would be a "fanfare" topic that signifies royalty, the hunt, etc. Similarly, a "march" topic could signify the military, patriotism, or some type of quest towards something to be achieved or conquered.
With this in mind, I think we can see explanations for each of these three listed ideas:
- Indiana Jones did serve in World War I, so a military topic is very fitting.
- Similarly, a patriotic topic is also fitting. (I even see some web results that make the claim that he's a great American patriot.)
- And of course so many of his stories are about quests to find some item or defeat some entity, which of course matches the march topic very well.
In other words, I don't think a march is limited to just the military or currently fighting for a government. Once we acknowledge a broader view of what the march topic may signify, it becomes much more clear why Williams may have chosen to write the theme as a march.
For anyone interested in topic theory, you may want to check out The Oxford Handbook of Topic Theory.