The RP Hypertrophy app is designed to maximize hypertrophy and so this means the more options for movements you have the better. With that said, you can absolutely take advantage of the app with a home gym. We do recommend having a baseline amount of equipment in order to take full advantage.
Equipment that allows you to accomplish hard training in your upper and lower body is best. This means that having a squat rack, bench, barbell, and weight plates would be a baseline standard to ensure you can get hard training at home for upper and lower body. This is not a necessity, again so long as the equipment you have allows you to train hard for each area of the body. You could likely get away with dumbbells only but again this can limit your options slightly.
The app does have a filter for identifying what types of movements you can do which should support you in having the app determine movements for you based on the equipment you have access to.