What does the term "relay competent" mean?
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.