In this paper we continue our study of nonlocal reaction-diffusion problems of gradient flow type that we developed in a previous paper [AHMM23] by using the notion of CP-structured reaction functionals as introduced in [AHMM19]. We consider here problems with times delays and DCP-structured reaction functionals as introduced in [AHMM20]. We present an existence result, investigate stochastic homogenization and provide an application to spatial population dynamics.