It's like this: Google has to keep growing to justify it's stock price. In order to do that it has to expand beyond search and ads. Google's technical infrastructure is the best in the world in many aspects, so they decided to open it up to other companies. However, other companies don't just come by themselves. That is why Google hired a bunch of sales people. Now these sales people do what they were hired for, they sell including to the government.
Tech companies tends to not just take over an existing market. But to grow it, by opening opportunities that didn't exist before. Like how smartphones created a market for apps, inventing a need that wasn't there before.
I don't see how that's likely to happen with military contracts. What beneficial need are they going to invent?
Google wants in so more senators lobby for them. Anytime you talk about cutting military budgets a whole load of people get on the news and talk about how you're hurting Americans with jobs. Google just wants in on the political action and guaranteed income.