Okay, first up, the term 'species'.
I don't want to sound all wanky, but it's a "human construct".
There are MANY definitions for what a species is, each has benefits and weaknesses.
For example, a common one is "can it reproduce with X, if not, they are different species". Many bacteria and fungi don't need to use sexual reproduction, so it doesn't work for them. Further more, when they do (eg bacterial conjugation) they can reproduce with just about any other bacterium.
Nowadays, bacteria are often catagorised into operational taxonomic units (OTUs), and the definition is usually specified. For example, I might define whether two bacteria are in the same OTU based on the %age difference between their 16s gene (it's often used to identify bacteria).
Why don't species exist? Because a species is a distribution of genetic diversity. It's like a bell graph. Two species might be like two bell graphs with different averages. There might be overlaps between the two. In fact, maybe two individuals can reproduce together, but two others can't. Species just aren't as fixedly seperate as we like to believe.
In bacterial alone, there are at least three major catagorisations used to determine the taxonomy. Some are functional, some are based on how you grow them in a lab, and some are purely genetic. What I can say, is that there are thousands (tens of thousands) of bacterial groups, which are considered as diverse as say, the entire 'arthropod' section of the animal kingdom. A gram of soil, might have 60,000 bacterial OTUs, based on genetic estimates.
So you are right, any one of Fungi, Bacteria or Archea, would absolutely swamp arthropods based on any metric (genetic diversity, number of OTUs, and even total biomass). However, they aren't within Kingdom Animalia
