to do that in real time, guitar rig will need more inputs. how can you have 2 sources(the guitar signal and the processed sound) going into the same input and record what you want to?
really, it's hard to interpret what's up in that project(maybe if the asio source connects were highlighted it might help), but it looks like you have the guitar going into channel 1 of the mixer and out the "direct out" of the mixer going into the asio source input one. this is the sound going into guitar rig.
then you're listening to the output from guitar rig(asio source1 l,r) in channel 2 of the mixer(input2) and coming out of channel2's "direct out?
nothing.
so, guitar rig is hearing only what comes directly out of channel 1 of the mixer, the dry guitar signal. in order to record the wet signal, you need another set of inputs(so that you can still put the dry into guitar rig to be processed) to connect the direct outs from channel 2 into. using guitar rig in the sequencer would make this job so much easier.
these connections and principles are identical to the real world, the same as connecting up to your amp and putting pedals in between. just follow the signal flow. you can also put scope effects in the chain, either as inserts or as modules in the routing window. the scope effects don't add any significant latency.

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you should check out dynatube, Celmo's GAM and Celmo's (free!) guitar bluesman. Celmo also makes a speker sim. these scope amps are just amps, you'd have to add effects(there's plenty of those and you've probably got pedals and guitar rig has them), but as
amps i think they're superior to guitar rig and line6.