It's all proportional. With 300 rooms, you' don't need a pool the size of the Boardwalks. Something more like a lap pool in a themed room. Massive wall of screens showing space outside and views consistent with what the rooms are looking at too.
Not sure about a Spa, but I would tend to agree that you don't need one. Then again, maybe some small facility. I'm not a spa person, so no good frame of reference for scaling it down.
For restaurants, size dictates again. I'm going to guess 1 or 2. You can probably get away with just 1. But, they might figure out how to stuff 2 in to allow for regular and premium dining. The premium one could be much much smaller, a boutique size within a boutique size. Could even do a single kitchen and just separate dining rooms and a different menu. High prices at the exclusive premium room that only seats 30 people.
I agree that I wouldn't expect grandiose shopping and business center. But, a gift shop of some sort is a guarantee. If nothing else, I've never been in a hotel that didn't have at least a wall of sundries standing in as the gift shop. A room's worth of space to buy your space souvenir seems expected. Along with a closet sized room that's the business center, basically a computer and a printer.
It's size again, at 300 rooms there's no need for extensive facilities.