Right. It has no integrated circuits. There's no way it doesn't have a computer. It couldn't receive signals and fire its thrusters otherwise.
A collection of discreet electronic components hardly qualifies as a computer.
Um...what was this, then? It wasn't even the first transistorized computer, let alone the first electronic computer (which would've used vacuum tubes to implement logic). It's a rather large "collection of discrete electronic components," with not so much as a 7400 to be found within its cabinets.
Even the smaller collection of components within ISEE-3 is able to act on radio input to control thrusters, instruments, and such, and to route instrument outputs to the transmitter to send them back to Earth. It might not have a general-purpose CPU controlling it, but neither did (for instance) many of the video games that were on the market around the same time it was under development.