I have a terminte/winged ant based insectoid species, but it doesn’t fit in well with the rest of the universe. I was reading the Darksaber book by Kevin Anderson and thought that the Taurills were a cool concept, as they were a non-insectoid hivemind. Yes, they had the problem of all getting distracted by a passing comet and such, but I was wondering if there was a way to explain evolutionarily as to why a species developed a hive mind. Especially, if they were mammals or other non-insectoids. Parameters: I would like to see that the organism is: non-insectoid, not a humanoid, and the organism is roughly a meter long, half that wide and has 8 legs.
If you mean "all the individual organisms are telepathically linked to produce a single coherent mind for the hive", then... even insects don't have hive minds. That's a pure fantasy construct. There are various ways that different sci-fi authors have tried to justify it in a hard-ish science setting (e.g., Vernor Vinge's Tines using ultrasonic networking, the aliens from Robert Forward's Camelot 30K having biological radio transmitters, etc.), but there's no particular reason that such abilities should be restricted to insectoids (and indeed, Vinge's Tines are more similar to dogs than insects).
If you just mean eusociality, where the hive behaves like one unified organism from a reproductive perspective, there is the real-world example of naked mole rats for reference. Just make the common ancestor of land-dwelling vertebrates on your alien world 8-legged instead of four-legged, evolve naked mole rats again, and make them slightly bigger (changing size is evolutionarily fast when you aren't running up against the absolute upper and lower limits), and there you go. If you want them to only have one mind, just make the development of self-awareness and higher intelligence dependent on sexual maturity, so only the queen of the hive has a mind, and orders everyone else around. (That's not how the social structure actually works in insect hives, but it kinda is for naked mole rats already.)
The hard part is the communication. If your SF is soft, you can just say that they are telepathic and leave it at that. How? Narrator doesn't know, reader isn't told.
Humans can be pretty hive-mindish at times. Watching a modern military unit operate can be both impressive and scary for this reason. They work as a UNIT, a hive.
For humans this is achieved through hard training. Other species can have a stronger group instinct and get there easier, maybe for their entire society.
An untrained group of humans can still become sort of a hive mind when they form a mob. However, mobs are stupid to the point where it is debatable whether they can be called a "mind" at all.
For a hive mind to form, most of the individuals must instinctually feel that the hive is more important than the individual. Soldiers are drilled in this.
For the hive to be smarter than the individuals they need good communication. Soldiers are drilled in this too. Mobs are not.
Species where one individual is very fertile while others are sterile has a head start, since the sterile individuals literally have no future except through the hive. Nevertheless, it is quite possible to get there through other paths, as the humans show us.
And insectoidness or not really has no bearing on the issue. Organisms on other worlds have no reason to follow the same paths as they did on this world.
Resistance is futile
The Borg seem to hit most of the queues you're going for. Adding a few legs to them and making them look different shouldn't be much of an issue.
Two caveats: One is that they are being controlled by a designated leader, i.e. Borg Queen, so not a 'hive mind' in the sense that it is not controlled by a single entity. But most examples of fictional insectoid hiveminds have some kind of queen, brainbug or Overmind at the top.
The other being that Borg are cybernetic organisms and their hive-mindedness is much to do with the implants they posess. This might be undesirable, but you're going to want some kind of explanation how the hive mind works anyway. Telepathy being the most common trope, of course. In the real world, I believe insect colonies coordinate largely based on pheromones and possibly electro-magnetic waves.
They are all one organism
And they are connected. What appear to be individuals are in fact organismoid appendages that are connected with one another and also with specialized individuals deeper in the hive. In the wet, cluttered environments where they live the slimy filaments that connect them might not be evident but it is there. The mental connection is not instantaneous - it might be at the speed of nerve transmission for longstanding connections or it might be slower.
If one of these apparent individuals is mechanically cut off from its hivemates it will cast about in an automatic manner trying to find the filaments and re-establish connection. Soldier caste organismoids have aggressive automatic behaviors that they can manifest when cut off - attacking any nonself entities in the area.
It seems to me that naked mole rats on earth have a social behaviour quite close to the societal organisation of insect hive-like species with queen, soldiers, workers. I would say that in order to evolve that way (and that would be consistent with the naked mole rat exemple), a species should just be in competition with species superior to it in terms of access to food and other basic needs. If the only options are to disappear or opt for social specialization, it can go that way. It’s not mandatory that it was the only evolutionary path, only that it was a possible one.
This already exists in some universes.
Here you have an example in W40K:
You can argue that they are insectoids but... not exactly.
Something kinda similar in Asimov's Foundation series:
Basically, telepathic hive minds do not really exist. In reality, is a well and long developed social behaviour that some species have. They feel (Maybe by sight, by motion or wathever) other individual movements or actions and they act accordingly for a greater objective. But they are still individuals. They are just constantly monitoring and sensing their surronding fellows to extract the information on what they should be doing. And this, to some extent, is also aplicable to humans.
So you are basically on your own. Whatever telepatic hive mind you create won't have a scientific foundation, and the real hive minds are certainly possible outside of insects. It is just the result of biological evolution. I would say it is more probable to happen to small size animals though.