To understand the purpose of the booby-trapped solar system we should recall what it is. The system is described as follows:
That star [in the Tecoma system] wasn’t natural, it was created. And it was created from a system that looked like Sol. It was manufactured and it was pointed at the ring gate. They aimed it like tying a shotgun trigger to a doorknob. Our bomb ship did something to activate it. Maybe it got something to come look at us, and that’s what set it off. I don’t know. But it was built to be a booby trap... It fired off the largest gun that it’s possible to make given the physical laws of the universe. And what’s more? The [Ring] station was built to withstand it. It took a gamma burst from a collapsing neutron star, and it’s not dead.
Elvi Okoye, Tiamat's Wrath, p. 212
While it's true in some sense that the Ringbuilders
pointed "the largest gun that's possible" at themselves, it's not really a danger to them because the Ring station was built to withstand it (as is apparent from when the booby-trap actually went off).
The reason why the Ringbuilders pointed it at the system's ring is hinted at by books 3-8, and especially once
ships transiting through the rings started "going dutchman".
Recall that Naomi figured out that this problem can be avoided by staying in the "safety curve", and that the
safety curve was based on the amount of matter and energy making transits though the gate network.
Tiamat's Wrath, p. 213
Up to and including book 8, multiple characters theorized that
the creatures that killed the Ringbuilders -- the unknown aggressors / Goths / "dark gods" -- are harmed or don't like the movement of ships through the rings, and that these enemies attacked the Ringbuilders to get them to stop using the rings. Furthermore, these enemies apparently attack through the rings -- hence the design of Duarte's attempt to attack them.
This turns out to be true. Leviathan Falls (book 9) reveals
It's where the power comes from. [The Ringbuilders] cracked the universe open, pushed their way in here, and it pushed back. A whole other universe trying to smash this place flat, and it powers the gates, the artifacts. That magnetic ray gun Duarte was playing with. They built stars with it. Broke rules that you can’t break without a different set of physics to strain it through.
The Investigator, Leviathan Falls, p. 453
In other words
the Ringbuilders forced open a space (the ring space) which is powered by another universe (where the Goths are from), and the use of this power from the Goths' universe is what angers them. Furthermore, this confirms that the Goths enter our universe from the rings / ring space, so in effect the Tecoma system booby-trap is also pointed at the Goths. Moreover, the Ringbuilders also knew or theorized that energy (and matter) passing through the rings harmed the Goths, so they pointed "the largest gun" they could at a ring gate. As a real-world analogy, this would be like the Roman army deploying catapults aimed at the roads they built (leading into their territory) to defend against invading barbarians (Goths) -- the weapon is pointed at the road the Romans built, but only because that's where the enemy will be coming from.