They are recompiled. First of all, Excitebike 3D Classics has a widescreen presentation (uses all 400 (or 800 in 3D) horizontal pixels), which is impossible with a NES ROM. Kirby's Adventure, while having a 4:3 presentation, the doorway graphic has been modified and now has a "light/shadow" thingy that goes waaaaaaaaaay over the NES's color limit (its like that even in 2D mode). Also some stages that take place in the sky have a gradient effect on the bottom, which wasn't in the NES version, not to mention that gradient color effect is clearly impossible on the NES. To create the 3D effect, the screen has to be rendered twice, and tiles have to be shifted left and right for each screen. If you did that with a NES ROM, then there would be blank tile space, but there isn't, because Kirby's Adventure 3D Classics isn't a NES ROM, meaning they added tile layers that weren't there in the original game in order to create the 3D effect. Also, with the NES's limited sound channels, when certain sound effects are played on the original game, parts of the music would temporarily cut out. This doesn't happen on the 3D Classics version, because the 3DS obviously doesn't have the same sound restrictions of the NES.
That being said, it's pretty obvious that 3D Classics are NOT emulated ROMs (I mean, seriously, just look at the new door graphic in Kirby), more like they took the original source code and actually ported (not emulated, ported) it to 3DS, then made changes as necessary. The reason why some 3D Classics (like Kid Icarus and Kirby's Adventure) still have a 4:3 presentation is because many things boss fights and minigames take place on backgrounds meant for a 4:3 viewing area, so it would be more work to draw areas that weren't there previously; also boss fights would feel weird if you could only move around towards the center of the screen.