High-index dielectric nanoparticles have become a powerful platform for modern light science, enabling various fascinating applications, especially in nonlinear nanophotonics for which they enable special types of optical nonlinearity, such as electron-hole plasma photoexcitation, which are not inherent to plasmonic nanostructures. Here, we propose a novel geometry for highly tunable alldielectric nanoantennas, consisting of a chain of silicon nanoparticles excited by an electric dipole source, which allows tuning their radiation properties via electron-hole plasma photoexcitation. We show that the slowly guided modes determining the Van Hove singularity of the nanoantenna are very sensitive to the nanoparticle permittivity, opening up the ability to utilize this effect for efficient all-optical modulation. We show that by pumping several boundary nanoparticles with relatively low intensities may cause dramatic variations in the nanoantenna radiation power patterns and Purcell factor. We also demonstrate that ultrafast pumping of the designed nanoantenna allows unidirectional launching of surface plasmon-polaritons, with interesting implications for modern nonlinear nanophotonics.