The Zelda style of gameplay is too basic to where it's close enough to any gameplay that has any similarities to it that people will say it's a Zelda clone.  As someone who's not a Zelda fan it's something that annoys me, but I see the reasoning behind it since while the game may not be not exactly like Zelda, it's got similarities.  It's a platforming version of Zelda where the games platforming is puzzle based.  Instead of pushing a block and hitting a switch, you'll jump onto a switch that opens a door instead.  Other stuff like killing all the enemies still applies, and finding certain ways to progress through the dungeon in order to get to the end.  The first area in Star Tropics you could lead yourself into circles was in the ghost town for example. 

The second game removes the puzzle based platforming in turn for skill based platforming, something that makes me think they felt that they couldn't do platforming properly so decided to use the preset platforming on the original as a crutch(which made it an awesome and very unique game.)  It's still got the puzzle elements, but not so much.  Even then, the game still borrows from Zelda, theh kill all enemies to clear a room, and there are still switches on the ground that open doors.

Star Tropics is one of Nintendo's best franchises in my opinion, and I was disappointed that they've never brought it back, but they're fine with bringing back a franchise I didn't care for.  Kid Icarus, but not an actual good game.  The reason I think that Star Tropics failed as a viable Nintendo franchise is that the sequel, Zoda's Revenge, launched in 1994, well after the SNES was released, and unlike their well known characters, Mike was just a normal kid.  The sequel was set up to be a failure from the start.  I actually got both the original and Zoda's Revenge the same day, brand new from a bargain bin(I think in KB toys,) so the original didn't sell well at all either.

Not sure if you're aware, but there's also Zoda's Revenge: Star Tropics 2 also on the NES. The scenes in the game were more of a comedy like how you're explaining, with Mike Jones(who?) getting pulled into other timelines with cave men, Cleopatra, Sherlock Holmes, etc, then making jokes about it.

The gameplay is the same but smoother, where you can move and attack in eight directions and have a controllable jump.  Mike also gets upgraded weapons rather than the Yoyo he's had from the first game.

I think if they were to update the series, it'd be best if they left it in 2D. But if they did update it to 3D it'd be best if the world was designed like Zelda 64 and if Mike Jones controlled similar to link but with his own weapons. Have other weapons still in the game, like the disposable baseball bats, berries, snow man ice attack, etc, but leave the Yoyo as his main weapon since a throwing weapon would make it too easy with a lock on style gameplay.

Bonus points for the first one to get what I mean in the parenthesis.  You don't get anything, just props, so pat yourself on the back.