The words "founder" is like "president" — its meaning is incomplete without the thing founded. You can talk about "the founder" but only when the thing that they founded is clear from context. It would be odd to say "He is a founder" unless we have already been talking about a company or organisation; or to say "I saw three founders together yesterday".
So the relationship between a founder and the thing they founded is a close one, and is marked by "of".
The situation is similar for "company director", but not quite so strongly: you can say "I met three company directors today". But if you are talking about a company director and the company they are a director of, this is the same close relationship, and you us "of".
Relationships marked with "at", on the other hand, are what linguists call "adjuncts": they give additional information (which might be very important in the particular sentence, but are not part of the meaning of a term).
So in most contexts, "the founder at ABC" would be incoherent. You would need a special context like "Our company was founded by two people, one of whom left us to go to ABC, but the other is still with us. The founder at ABC..." for it to make sense.
For "company director", the situation is less clear-cut. You can certainly say "He is a director of ABC" — and I would not use "company" there, because the thing that he is director of is ABC, a company.
You can also say "He is a director at ABC", but that implies that he is not a director of company ABC, i.e. that he is some other kind of director there — perhaps director of marketing.
"He is a company director at ABC" reads a bit strangely to me, but I would accept it, especially with a comma "He is a company director, at ABC", where the "at ABC" reads like an afterthought.