Is it possible to build a regression model for predicting movie gross using sections on their wikipedia pages?
If your models suffers from multicollinearity problems, then yes, I'd say go for dimensionality reduction (possibly non-linear, such as t-SNE or Autoencoders). Moreover, 100 variables for 650 observations is a lot, I would apply a much more drastic reduction, but that's up to your preferences.

If your model is overfitting excessively, then I suggest you to try Neural Networks with high dropout probability. That helps a lot in preventing overfitting. Also, try other models, the more you try, the more confident you'll be about results.

Please keep in mind that normally Neural Networks require a lot of data to perform very good. If you have just 650 observations, tree-based models (Random Forest Regressions or XGBoost Regressions) could work even better than Deep Learning. They are ensembles of trees, i.e. desgined to combat overfitting, and could capture non-linear patterns of your dataset.