The linac of the European project Extreme Light Infrastructure-Nuclear Physics (ELI-NP) foresees the use of 12 traveling wave $C$-band accelerating structures. The cavities are 1.8 m long, quasiconstant gradient, and have a field phase advance per cell of $2\ensuremath{\pi}/3$. They operate at 100 Hz repetition rate, and, because of the multibunch operation, they have been designed with a dipole higher-order mode (HOM) damping system to avoid beam breakup. The structures have symmetric input and output couplers and integrate, in each cell, a damping system based on silicon carbide (SiC) rf absorbers coupled to each cell through waveguides. An optimization of the electromagnetic and mechanical design has been done to simplify the fabrication and to reduce the costs. The cavities have been fabricated, and the first full-scale prototype has been also successfully tested at the nominal gradient of $33\text{ }\text{ }\mathrm{MV}\mathrm{/m}$, repetition rate of 100 Hz, and pulse length of 820 ns. It represents, to our knowledge, the first full-scale linac structure with HOM damping waveguides and SiC absorbers tested at this high gradient. In the paper, we illustrate the realization process of such a complicated device together with the low and high power test results.