The default view of the EIGRP topology table actually does not contain ALL paths to a network. You'll see a next-hop if it is either a successor, or a feasible successor. If a certain path doesn't qualify as either of those, then it doesn't go in the topology table.
EDIT: As another answer correctly points out, you can use the "all-links" argument to get the topology table to list every potential next-hop. EIGRP will still need to re-compute DUAL to guarantee a loop-free topology, but this way you can at least see the non-feasible and non-successor routes.
This is different from OSPF (at least within an area), where the "topology table" (the OSPF Link-State Database) contains all information about the network.
When a route goes active in the topology table, it is because it has neither an S or a FS. An active route is actively asking the network for valid next-hops to reach said network. In this case, the metric to your loopback network from R1's perspective through R3 is considered not good enough to qualify as a FS, so it merely installs the single route through R2 into the routing table as a successor. If this path were to fail, the route to 18.104.22.168 would go active, and R3 would respond, saying that it is able to offer reachability to this network the long way around.
R3 uses both potential paths because your metric weights make it so that only delay is used in the metric computation. So, from R3's perspective, the two paths to the loopback are equal-cost, so both are successors (see your topology table?)