They should, but they don't. This is what creates what some call "power creep". Certain champions become less potent based on new champions that come out. It'd be extremely hard to rebalance everything with every new champion, which is why competitive games should really be derived from the players and their choices, rather than a set roster of existing builds.
I skimmed through and misread your question. The "balance" part threw me.
No, they don't. Games run on what's called an "engine", which basically is a system of programming shortcuts that allow them to design the game more efficiently. Game engines allow developers to, for example, tag specific code ingame as an ability, a basic attack, a shield, etc. Thus, when they make a new champion, they would simply say that all of their abilities classify as abilities, and because Sivir's shield blocks abilities, it'll automatically register that "Hey, this gets blocked!"
Likewise, if a new item with an on-hit effect is implemented, because Yasuo's Q is designated as a basic attack, the on-hit effect automatically applies with no extra coding.
It's probably not exactly like that, as it varies by engine, but that's the principle.