Okay. Here is what I see.
I do not see any reference to dropping ratings from the SERPs for charging an entrance fee.
The article and Googles announcement do not seem to mention this.
Both, the article and announcement mention the name property is required. Where both are confusing is that there are more mark-up schemas that include the name property such as place. Place allows for events, reviews, and opening hours. Tourist attaction also allows for events, reviews, and opening hours.
The events allows for offers which can include price.
Following this, it appears that both place and tourist attractions would be allowed according to the announcement where a charge could exist (with one caveat to follow), however, what is confusing is that these schemas are not included in the list.
I have only to conclude that these schemas are allowed to have reviews and charge a fee and that would make complete sense to me. One caveat exists. In both the article and announcement, the reviews cannot be handled by the site itself or by a widget on the site. While I personally do not agree with this, reviews from another site without using a widget may be used. I am, unfortunately, not familiar enough to know how this would work. For example, can you have Yelp reviews without a widget? Perhaps a WordPress plug-in exists that can help for WP users. What other options exist? Who knows.
It is not clear where the line is drawn even with what appears to be simple rules. You are right to be confused. Personally, thinking about local attractions, I cannot see why an attraction should not have reviews. I am just as confused as you are.
The only thing I can see to do is to try it without soliciting reviews on the site or through a widget on the site and see what happens.