Unpopular (?) opinion - text/IM systems are asynchronous messaging systems, and in most cases it's totally reasonable to not immediately jump on your phone and answer a message as soon as you get the notification.
One of my friends is the sort of person who will stop mid sentence when their phone pings so they can answer whatever they've been sent and it drives me nuts
If it's recently, its probably helldiver's 2 in which case wait your fucking turn lady! He's risking his life to spread liberty and force democracy on godless bugs and soulless robots. THESE ARE IMPORTANT THINGS
At one point in college some friends and i made up a system for just explicitly state what sort of response you needed. Ok, "made up a system" is a little over stating it. Basically it was "Hey this is important can I have your undivided attention?" through the lens of stupid nerd jokes. Like, "setPriority(10) i'm locked out of my apartment do you have a spare key?" vs "setPriority(0) i am so mad that fallout3 requires GFWL"
Now i'd probably just say "hey this is important do you have a few minutes?" in normal words.
Oh I'm busy doing some other aspect of my life. Might possibly be that I'm working, at my job, which by the way was one of your requirements on the dating profile.
Not absolutely everything in my life is about video games.
Whenever someone sends me an important message and I don't read/respond in time, they call to get my attention so I can do so. My ex used to get mad at me for "ignoring" her for 2h or more and would call. I was just busy doing whatever and ignoring the phone as usual.
For an average guy, you'd be lucky to get more than one convo.
As another user mentioned, there are bigger priorities at the moment on top of texting-- like you're working. And personally, I don't like texting especially with crappy autocorrect of phones. I prefer speaking in person.