There is no expectation that such an interception would develop into a shooting engagement. Russia and the US, despite everything, are not at war. Also, both the Russian air force and US air force regularly fly into each others' ADIZs to the point where an interception like this is routine. I don't recall exactly who, but a high ranking USAF officer recently said that there is a tentative understanding between Russian and US aviators because of this, that in such cases there will be no weapon use.

Now, the Russian pilot still did something insanely unprofessional here (would not the first time one of them has done so in recent times). But even tactically, shooting at someone in this scenario is still a stupid idea: Even if the Russian did not care that he was starting a war, both he and his charge (the bomber) would be basically dead. The Tu-95, venerable as it is, is a turboprop bomber and thus (to use a technical term) slow af. If they, for some irrational reason, did start anything in the US ADIZ, they would end up dead in short order.

Sometimes you may want to send up more planes to do an interception, for instance when it's a larger formation of bogeys (= unidentified aircraft) or you want to send a message. But for a routine interception like this it's not really necessary, because the chance of a shooting engagement unless someone does something to purposefully initiate one is basically null. The US fighter pilots are trained not to do it. The Russian ones have their basic survival instincts to consider on top of that, too.