Quantitative data that varies discretely and arbitrarily along some scale can be called count data.
Nick Chrisman (1995; Beyond Stevens: A revised approach to measurement for geographic information, presented at Auto-Carto; see this PDF for a transcript) pointed out that there are many more typologies of measurement than the 'classic' four proposed by Stevens and outlined in Wikipedia's Typologies of measurement article.
None of the measurement typologies are rigid or prescriptive, but Crisman is not alone in recognizing counts as an important statistical data type:
Another class of geographic measurements consist of counts aggregated
over some region in space. Counts are discrete, since there is no half
person to count, but a count captures more mathematical structure than
the other discrete levels (nominal and ordinal).
Mosteller and Tukey also called them counts (see Mosteller's book, Data Analysis and Regression).
It's clear to me that the concept is a good fit for, say, population, but your biomass example seems intuitively less clear-cut. The point is that it's a countable quantity, as opposed to a ratio scale, so it might just be a matter of being careful how you define the term.
This answer was edited after clarification in the comments.