I'd say they're more algebraic representations of regular geometries.

Algebraic Geometry as a mathematical field is interested in solving highly non-trivial geometric problems (think, from differential geometry, functional analysis, etc.), using tools from Abstract Algebra (think Galois Fields, Lie Groups etc.)

It saddles a bridge between traditional geometry, and abstract algebra, and allows insights from one field of mathematics to be applied to the other. As such, it allows practitioners skilled in these tools to make many useful inferences about incredibly complicated systems.

It's also incredibly dense. In part because many of the tools of algebra are incredibly involved. But also, in part because to define an algebraic object in a way that is equivalent to a geometric object, sometimes requires a fairly complicated definition.

Algebraic geometry existed before Grothendieck lol. It's still algebraic geometry even it looks boring next to etale cohomology of infinity stacks or whatever.

Even before Grothendieck's scheme theory, algebraic geometry was already pretty focused on varieties in rings of polynomials and other such constructions.

The heart of the domain is still using abstract algebraic arguments to solve geometric problems.

E.g.; Euclid's method for finding the midpoint of a line is to draw two concentric circles centred at the vertices with radius the length of the line. The straight line that passes through the two intersection points of the circles, also passes through the midpoint of the line.

This is the same as saying the midpoint of a line is the intersection of an algebraic variety with a root at one vertex, and another algebraic variety with a root at the other vertex.

You don't need schemes, or projective curves, or local rings to prove it.