From your description, it sounds like you want either the Pro plan with Zero-Downtime Failover or LoadBalancing.
Zero-Downtime Failover is a simpler solution, but one which you have less control over. You essentially add a DNS record pointing to each server. This means that some traffic will go to one origin and some to the other, usually around 50% but it’s not exact. This required a paid plan.
Load Balancing gives you far more control over the setup, you can have multiple origins in different pools and choose whether you want traffic to be split between origins or only go to the second if the first is down etc. This is an add-on and is billed based on usage.
It depends on exactly what you want to achieve, but those are the two you should look at.
If this is what you want, you need Load Balancing as described in the docs you linked to.
The current Argo product (Smart Routing) is faster routing through the Cloudflare network. For long-distance visitors, if Cloudflare can route traffic internally faster, it’ll do it. It is not involved in load balancing.