I am not sure this is neomutt's fault or chromium's. It looks like the
root cause is xdg-open not respecting Terminal=true in neomutt.desktop.
There is an existing bug about that:
https://bugs.freedesktop.org/show_bug.cgi?id=92514
Wrapping the neomutt command in a terminal emulator works as a
workaround for this specific bug, but is a bad fix in general since it
would create a second, redundant terminal if launched from anything
other than xdg-open.
I thought mailto: links used to work for me in chromium... I am not sure
if something changed (probably in chromium) or if I imagined that.
BTW the reproducer can be even shorter: just enter
mailto:some...@example.com in the address bar.