You are wrong. They do say there is a modified response - but they raise no alarms and don't state or imply that this leaves the person immunocompromised. One could infer that, but without information on the degree and duration of the suppression, it is just a guess.
From the papers conclusion:
BNT162b2 vaccine is clearly protective against COVID-19, but the duration of this protection is not yet known, and one could envisage future generations of the vaccine incorporating this knowledge to improve the range and duration of the protection. Our findings need to be confirmed by conducting larger cohort-studies with populations with diverse backgrounds, while further studies should examine the potential interactions between BNT162b2 and other vaccines.
The full text of the conclusion statement:
In conclusion, our data show that the BNT162b2 vaccine induces effects on both the adaptive and the innate branch of immunity and that these effects are different for various SARS-CoV-2 strains. Intriguingly, the BNT162b2 vaccine induces reprogramming of innate immune responses as well, and this needs to be taken into account: in combination with strong adaptive immune responses, this could contribute to a more balanced inflammatory reaction during COVID-19 infection, or it may contribute to a diminished innate immune response towards the virus. BNT162b2 vaccine is clearly protective against COVID-19, but the duration of this protection is not yet known, and one could envisage future generations of the vaccine incorporating this knowledge to improve the range and duration of the protection. Our findings need to be confirmed by conducting larger cohort-studies with populations with diverse backgrounds, while further studies should examine the potential interactions between BNT162b2 and other vaccines.