While other answers address the specifics of the example games given, there is actually a couple of different subtypes of games that would also apply to 'Game that has other games within it' that I think is worth covering:
These are games where the entire goal/intent of the game is to overcome a wide variety of puzzles and challenges.
There may be little to no game mechanics outside of the puzzles/challenges. Plot/Story may non-existent, or only exist in a bare-minimum fashion to drive some sort of progression & unlock more or harder minigames/challenges.
While Wikipedia calls these 'Minigame Compilations', A large subset of games in this category would also be classified as 'Party Games', and purely singleplayer versions may also be referred to as 'Puzzle Games'.
Note that not all 'group-play' games are minigame compilations (eg. Mario Kart), nor does every Puzzle game feature multiple different minigames (eg. SpaceChem), so your partner may not be able to use 'Party Game' or 'Puzzle Game' for her academic paper.
Some examples include:
See also: Wikipedia's List of Minigame Compilations
Game Packs & Collections
This classification is where the outer game acts as more of a 'launcher' for a collection of larger games (rather than minigames/challenges).
These types of games are generally called 'Packages', 'Packs', Compilations or 'Collections', the marketing folk among us would probably call it 'Product Bundling'.
Some examples include:
- The Jackbox Party Pack - a collection of trivia-likes and other group/party games.
- Rare Replay - a 30th anniversary collection of Rare video games (Rare the company, not as in common vs rare).
- NES/SNES Mini/Classics - reproduction consoles loaded with classic Nintendo titles.
- Mega Games 6 - A '6 in 1' compilation cartridge for the Sega Genesis/Mega Drive
- Various 'Sega Mega Drive Genesis Collections/Packs', eg For PS2, and For Windows/Steam. - Because one can not own enough copies of Sega games.
See also: Wikipedia's List of Video Game Compilations.
The features of the 'outer game' can vary greatly, depending on the implementation. Most will have basic 'launcher' stuff like the ability to browse games and tweak some minor graphics and sound options, but other features can include:
- Advanced graphics & sound - Scanlines & filters, colour/palette swapping, zoom/scaling, aspect ratio manipulation etc
- Achievements and Challenge Modes
- Progression/unlocks - eg. 'behind the scenes', concept art, cheats, mods/tweaks, bonus levels and even occasionally entire 'hidden' games.
- Pause, Save state and 'rewind' functionality that may have not been possible on the original game.
- Cheat engines and Mod integration
While larger games containing incidental minigames may not have an explicit name, there are games out there that almost purely focus on this idea, and those can be grouped and named: 'Minigame Compilation', or loosely 'Party'/'Puzzle' Games' would generally fit this scenario. While not quite what you're after, Game Compilation or Pack is also worth noting due to following a similar concept but with more rich games than just puzzles and challenges.