Problem is Indiana Jones movies are open world. They seem scripted to us, but to Indiana he's traveling all over the world, all the time, doing basically whatever he wants.
But they're not. He's going to the various set pieces for very specific reasons. Go to Tibet or wherever to get the medallion from Marian. Go to Cairo to get medallion translated by his friend. Go to desert based on information on medallion. Go to nazi camp to save ally and stop them from getting the ark, etc etc. He's not just wandering around and randomly coming across Redneck McHickson and his inbred family of moonshiners, and stopping to have a 30 minute debate with them about whatever stupid shit they think is true or whatever. Those movies are the epitome of linear storytelling, and sequential narrative structure. It's one reason they are so classic, because it's a tried and tested method of visual storytelling. And that translates most accurately in a video game, as an action adventure like Uncharted.
So if the goal is to try and actually replicate the spirit of an Indiana Jones movie, and not just slap an Indy franchise skin onto something for marketing, you'd want it to be at least somewhat like Uncharted.
If you just want to say "It's an Indy Jones game! Buy it!' then sure, make it sandbox, but it won't be like the films, not at all.
. There really isn't a good way to translate that into a video game that doesn't invite an unfavorable comparison to Uncharted and Tomb Raider.
I agree, though considering those games were inspired by Indiana Jones, I don't really consider it a bad thing if they are similar, that was on purpose by the teams making those games.
What type of game would you put Indiana Jones in that doesn't just copy those previous titles?
I honestly don't know. I haven't really ever thought about it. Because frankly I don't think it should be done. I personally feel, as someone who is the primary, target demographic for these nostalgia franchises, that they need to just be left alone, and people should come up with new stuff. Trying to capture lightning in a bottle, from a film series that didn't always have great entries itself, and then try and translate them into a video game, that is simultaneously in the spirit of the era they were based, AND when they were made, AND also accounting for modern sensibilities, is an exercise in futility. Something is going to have to give somewhere, and piss someone off. If they make the game design to feel like one of the films, it's probably going to be something like Uncharted, and that's going to make some players be like "Ugh, just an Uncharted clone with an Indy skin!". If they make it a sandbox, aimless, open world game, fans will be like "This isn't Indy at all! It's just RDR2 with an Indy skin!" If they try and make it an FPS, well, I don't see anyone really liking that, as Indy did very little shooting in those films, compared to punching and swinging about.
So I have no idea what would be a good idea for an Indy game. I think it's probably doom to failure in some way. That at best, it's going to be "meh, it's ok" One of those games you forget a month after release for something more interesting. Though it's shelf life online will probably last much longer, as YTers will post videos with tags like 'How Bethesda MURDERED Indiana Jones in Cold Blood!" probably with a picture of Daisy Ridley looking upset, because they love putting her face up there on everything they want to cry about.