No, that's not a LAN based computer. But it could be a SMP structure which having a special scenario looks like a LAN.
Most HPC could be network linked multi CPU system, the network can be full mesh, SMP or hypercube which having different bandwidth and efficiency.SMP having issue when the CPU numbers goes high, usually when it goes above 20, the performance that the added CPU brings would be eaten by system cost. So design a new topology of links become a very challenging job for HPC designers. Since it need to consider what kind of O/S could be suitable for installation and provisioning in a parallel system.
At very begining, the HPC usually using a single CPU to get the system performance. But now, single CPU system is almost extinct, such as Cray, Thinking Machine, etc.