It sure looks like it. This is Challenger, a Famicom game released in 1985 by Hudson. Look at the cover art and you'd be forgiven for thinking this was some shitty Lucasfilm clone, lifting its two biggest properties and dropping them in an unlicensed video game rip-off.
That would be a little harsh.
Sure, at first glance there are similarities. The main dude has a definite Indiana Jones vibe to him, which is understandable, since Challenger is an archaeologist, just like Dr. Jones. But Princess Leia's trademark "buns" soon turn out to be more of a traditional Chinese outfit, and what first looked like Darth Vader soon begins to look more like a Samurai Mazinger Z (fitting, as Samurai armour was the inspiration behind Vader's costume design in the first place).
Still, for the fun of it let's roll with this being Indiana Jones fighting Darth Vader to rescue Leia.
Challenger, whose opening stage is a remake of sorts of a 1983 Hudson computer game called Stop the Express, is notable for two reasons. The first is that it's got a cool feature where it's basically four games in one, the action split across platforming, action and even a Zelda-like overworld section.
The second reason? The game didn't have two difficulty levels. Or three. Or even four. It had sixteen, Challenger allowing the player to, VGDen says, "increase the number and type of enemies the player encounter throughout the game".
Challenger was later re-relased on mobile phones, the Game Boy Advance and Wii Virtual Console, though sadly only in Japan.