If you read the lines immediately following your quoted line (on p.391, left column, last paragraph in the linked article) it becomes clear what **relay competent** means (and I quote):
> As a result, the cells sense and move toward a source of cAMP, and they **relay the signal as well by secreting cAMP**. [..] After about 8 h of starvation randomly located cells, called pacemakers, begin to emit cAMP periodically (Raman et al. 1976), the chemotactically competent cells move toward these pacemakers, and eventually the entire population forms a mound-shaped aggregate of up to 105 cells.
In other words, starvation makes cells move toward cAMP by chemotaxis, and makes them **secrete cAMP** as well, which factually **relays** the cAMP signal back to other cells that are also attracted to cAMP due to starvation.