>>43682469GBA software emulators don't run super well, yeah. However, all variants of the (3)DS have the GBA architecture on-chip, so they're able to natively run the games, even if there is no dedicated GBA cartridge slot. It's a lot like how later Wii's and the Wii U can't read GameCube discs, but since the Wii's hardware is more or less identical to the GC (and the Wii U has Wii hardware onboard), they're able to natively play games through homebrew like Nintendont.
GBA VC on 3DS (what the Ambassador exclusive titles use) utilizes the GBA hardware, and since it was officially made by Nintendo games run nearly identically. Why they didn't bother releasing any other games with it, I'll never understand. The DSi didn't have anything official like this, so instead you can use a homebrew program called GBARunner. While games run fine, audio isn't implemented properly: it sounds wonky and lags behind the visuals. The program is early in development, however, so hopefully this improves with time.