How could there be a higher dimensional, shorter path between the points?

Wolfram speculated on this idea: if spacetime is a graph, it may approximate the 3+1 topology on average, but in some places two distant nodes can be connected by a direct link. I'd speculate further that such isolated links may be enough to entangle low-level quantum properties of two particles, but not enough to be a tunnel even for a single photon.

That would not be a euclidean space.

Who said our universe is euclidean? We just make this assumption for convenience.

The comment I replied to initially.

Why does the path have to be shorter?

How would it be relevant if it's not?

Is the assumption that a signal needs to travel and that the speed of light is the limiting factor? My thought was that they're interacting in some other fashion, such that they are physically connected to each other. If that were the case, it would be instantaneous

Interaction via a hidden physical connection would only be instantaneous if that connection were zero length and only apparently faster than the speed of light when the connection is shorter than the shortest apparent path between the two points.