The games you've stated are very simple in design, and are extremely easy to "win". Some people might argue they can be complex (ie. chaining properly in Tetris and Bubble Shooter), but at the end of the day, it is their simplicity and low entry levels of difficulty.
Following the examples you've stated:
- Tetris has you rotating blocks that fall down the screen to create lines. They fall slow enough at Level 1; there is ample time to think before it reaches the bottom.
- Bubble Shooters have you shoot balls to create groups of a color to clear them; it is easy for the same reasons as Tetris.
- Solitaire has you drag cards until they follow a certain set of rules. The controls are really simple (just drag and drop), but the ability to know what moves to take on the other hand, may not be as simple.
- Pokémon Go (a more recent example) has you walk around*, tap on monsters and then throw (swipe) balls at them. It is both easy and simple.
* the elderly may find this difficult to do often and for long periods of time as required by the game.
It's also worth noting that both Tetris and a Bubble Shooter are not board games, per say.
Unlike younger people, who are open to learning, can discover patterns easily and are open to more complex gameplay ideas, or things that would have need us to actively think and be aware (ie. spatial awareness in shooters), the elderly may have difficulty grasping such concepts maybe because:
- They don't have the mindset or experience that most of us younger, modern gamers have.
- Their mental capacity/reflexes aren't as high (or fast) as, for example: a teenager, or an adult around the age of 40.
And with anything, there are of course some people that are exceptions to the above.