Based off a quick cursory search, check_nrpe_1arg is nothing special compared to check_nrpe, it has a bit of a backstory too.
check_nrpe by default does not accept command line arguments to be sent, just the command_name to run on the remote NRPE server host. In order to get NRPE to accept arguments beyond that (if memory serves), you have to enable a compile-time definition, AS WELL AS configure it in check_nrpe as well as the NRPE server
check_nrpe_1arg appears to be a mnemonic that is configured into the core NAGIOS
commands.cfg file; specifically, telling the installer that this command will accept only 1 argument (the name of the command to execute on the remote host) and will not honor any additional arguments.
It's a weird way to do it, given the default behavior of NAGIOS, but it gained traction nevertheless.
The quickest answer to this:
check_nrpe_1arg does exactly what it is configured to do in
commands.cfg on the core NAGIOS server. In this context, it provides the command name to execute on the remote NRPE server, and nothing additional will be accepted.
Also, it appears to have originated out of the default configs in "Untangle" (a Linux based firewall/routing software package), that or Debian, it's hard to tell without following a handful of links around.