Isso foi corrigido pelo chmod como usuário não sudo devido à configuração específica de permissões nesta máquina corporativa.
> chmod 0664 shiny-server-1.5.3.838-amd64.deb
> ls -al
total 83140
drwxr-x--- 3 tom users 4096 Mar 16 07:23 .
drwxrwx--x 5 tom users 4096 Mar 16 08:26 ..
-rw-rw-r-- 1 tom users 70643942 Feb 25 03:23 shiny-server-1.5.3.838-amd64.deb
>
> sudo gdebi shiny-server-1.5.3.838-amd64.deb
Enter password for tom (INTRANETPASS):
Reading package lists... Done
Building dependency tree
Reading state information... Done
Building data structures... Done
Building data structures... Done
Shiny Server
Shiny Server is a server program from RStudio, Inc. that makes Shiny applications available over the web. Shiny is a web application framework for the R statistical computation language.
Do you want to install the software package? [y/N]:y
Selecting previously unselected package shiny-server.
(Reading database ... 81902 files and directories currently installed.)
Preparing to unpack shiny-server-1.5.3.838-amd64.deb ...
Unpacking shiny-server (1.5.3.838) ...
Setting up shiny-server (1.5.3.838) ...
Creating user shiny
Adding LANG to /etc/init/shiny-server.conf, setting to en_US.UTF-8
shiny-server start/running, process 8854
>
créditos - sugestões de @steeldriver, @bistoco