The relevant passage is below. Basically it's a funnel, so It takes testing a large amount of people to tease out just a handful of infections. 162 cases for placebo vs. 8 in the vaccine group.

Analysis of the data indicates a vaccine efficacy rate of 95% (p<0.0001) in participants without prior SARS-CoV-2 infection (first primary objective) and also in participants with and without prior SARS-CoV-2 infection (second primary objective), in each case measured from 7 days after the second dose. The first primary objective analysis is based on 170 cases of COVID-19, as specified in the study protocol, of which 162 cases of COVID-19 were observed in the placebo group versus 8 cases in the BNT162b2 group. Efficacy was consistent across age, gender, race and ethnicity demographics. The observed efficacy in adults over 65 years of age was over 94%.

The 200 you mention are comparable to the 6 in the comment above, not the 152.

The problem is the confirmed cases are the primary part of determining efficacy. The people who do not get the virus have a smaller impact on that statistic at higher numbers. EDIT: User runamok explains it well.

[1] https://www.cdc.gov/chickenpox/outbreaks/downloads/appx-f-in...