There's no priority claim for the word "riparium" or the general concept of growing plants above the waterline in a fish tank by me or anybody else that I know of, but the particular configuration of planters and/or trellis rafts in the Riparium Supply product line and their use in an aquarium system has patent pending protection.
With the definition that we have been using here what you are describing sounds to me like a riparium. It sounds to me like it could work well for certain kinds of plants and would probably provide excellent biological filtration. Some kinds of plants that I have used can grow very well with their roots right in the water so an open-cell foam could be a good substrate for them.
Here are some of the ones that I think would be good for growing like that...
- Anubias (for high humidity)
- Java fern (for high humidity)
- peace lily
- pothos vine
- various emersed aquarium stem plants
I understand that in Europe hobbyists have been doing this kind of planting in combination with their hamburg mattenfilter systems for years already.
Some of the best riparium plants are more demanding of rich root fertilization and they are better planted in a clay-based gravel, so something more like a planter cup or a paludarium with soil substrate is better for those.