From my testing, it appears, that HUP or signal 1, like pkill -HUP chrome does lead to the same message, but issuing signal 2 to Chrome is a valid solution.
I, originally, have thought, that such a solution could be generic to all GUI programs. However, it likely is not. I'm, however, pleased to see this simple solution, which is:
pkill -INT chrome
or
pkill -2 chrome
one and the same command, just the first is the name of the signal instead of its number.
If we apply this solution over SSH with for example using an alias ssh-tv to connect to that laptop, we could define something very similar to this to achieve our reboot without that message:
alias reboot-tv-laptop='ssh-tv -t "pkill -2 chrome; sleep 5s; reboot"'
Note, that there may be many and maybe even better ways of achieving the same goal. This works for me personally.