Image content influences men's semen quality [2005]

"Nevertheless, the within-subject analysis suggested that, after controlling for differences between men, image content may not influence sperm concentration"

So apparently neither this, nor later studies were able to conclusively prove sperm competition in humans, but they weren't able to disprove it either due to methodological limitations, namely ethical constraints. The effect is potentially destroyed by the use of condoms as recommended by the WHO when collecting samples. If the subjects weren't humans the researchers could select different number of males with whom a female copulates and measure which sperm fertilizes the ova, but that's not something anyone can volunteer for.