You should use the testing build I released in another topic instead of the TILP II 1.15 one, because the testing build has a newer driver that is signed
But installing TI-Connect and TILP, or TINCLS/TINCS and TILP, alongside each other and have them both working "at the same time", will require some configuration.

Was it because I was using a serial link cable (black TI-Graph Link cable from TI)?

Yes

The problem is with USB devices, which need drivers: Windows doesn't like having more than one driver for the same piece of hardware (same Product ID / Vendor ID). TILP and TI-Connect / TINCLS / TINCS cannot use each other's driver, for licensing and trustworthiness reasons.
Using the filter driver helps, but this wasn't possible/safe on all Windows versions until the upgrade of the libusb0.sys / libusb0(_x86).dll performed for the testing build of what will become TILP II 1.16
And since, nowadays, computers with a DB9 or a DB25 connector are a minority, in practice, what happens is that without the USB filter driver, TILP and TI-Connect / TINCLS / TINCS can't be simultaneously in a working state on a given computer.
With the filter driver, they can (assuming that one manages to configure it to work properly - the process is still unclear to me, I'll browse the DUSB gCn documentation).

For completeness, let's mention that all linking software is claiming exclusive access to the target calculator; TILP and TI-Connect / TINCLS / TINCS cannot access the same calculator concurrently, but they can do so when the other one is not running.

You're welcome.