You know that klayout is a layout, not a schematics tool, right?
To get a layout to extract as a netlist may be "doable" but require
a lot of groundwork (recognition / extraction rules) to create such
a netlist. And that picture seems to lack a lot of connections that
a functioning SPICE netlist would want (power, inputs, outputs).
The simulation complaint window is one I have not seen (as I
use Xschem for schematics, which is a more appropriate tool when
layout details do not drive simulation - though photonics in the
present day, is not really that). Whether you can, by heroic effort,
make klayout cough up a layout-geometry-driven netlist / models,
I couldn't predict. But I can predict it will be a long hard slog with
a lot of questionable data to turn into formulas for models and
values.
There is no Figure A in the linked article. What you show looks
not much like Figure 1. So that's another thing.
It seems there -is- (contrib) support for photonics layout and in
the linked page for "Klayout" (which seems to be a side branch).
There are sub-links for "how to use" all that "stuff". You may find
very few mentors for this "path less taken" and the actual klayout
forum would probably be a much better place to ask (try with
better material to work from). The SiEpic (?) folks may also have
a useful forum (or failing that, their git page might have some
discussion / feedback you could use).