No, you can't do everything with just data structures. Everyone knows this. 1st-year junior programmer knows this. It's obvious. The original question did not talk about this, you misunderstood the level of analysis it was aiming at.
The fact that SQL is not turing complete is a meaningless truism here, because Linus obviously did not mean that we should all start using SQL instead of C. The point he is making is that data structures are of much bigger importance to get right in order for the program to be good. Not just fast or just maintainable, or just easy to understand. But all of those things and many others.
Of course one can force anything into a relational database. The data analog of "Turing tarpit".
Ironically graph databases are way better for describing relations than relational databases.
> Ironically graph databases are way better for describing relations than relational databases.
How so?
Easily represented as a vertices-array and an edges-array. It's conventional to index the (directed) edges to optimize iteration over all edges from a given vertice. If you're being "sloppy", you can also represent edges as vector<vector<int>> (one array of destinations per source). This is more convenient but comes with the slight disadvantage that these arrays are physically separated (for example, you'll need two nested loops instead of only one to iterate over all edges).