That's what I thought, but it was so shocking and sudden, I had a hard time processing and accepting it.
That gets back to Bourne's, and the other agent's/assassin's "training", ie brainwashing.
We got a job.
What kind?
The Forever Kind.

He'd been defeated and rather than risk being captured and questioned, either by Bourne or the cops who were on the way, he decided (or more likely had been trained/conditioned) to kill himself.