Can VSQL be used by other than dbadmin users?

Yes. it can be used by other users. You need to use -U while running the vsql command

-bash-4.1$ vsql -U test
Welcome to vsql, the Vertica Analytic Database interactive terminal.

Type: \h or \? for help with vsql commands
\g or terminate with semicolon to execute query
\q to quit

INFO: Connected to localhost at port 5433.

test=>

https://www.vertica.com/docs/9.2.x/HTML/Content/Authoring/ConnectingToVertica/vsql/CommandLineOptions.htm

Sruthi, I am able to access the database via DBVis, but using vsql, I get:
vsql: FATAL 2248: Authentication failed for username

Please double check the password you are typing in.. if it still fails with vsql but works with DbViz... please open a support case with screenshots and logs.

Thanks Will do. Yes, password is correct.

One theory is that you have an authentication method that is preventing this. For example, it is possible if you tried vsql locally that an authentication rule prevented it whereas DBVis worked because it was not a local attempt. Here is an example where user "doug" is rejected locally but not when I provide a host. This is due to an authentication rule that prevent this user from connecting locally.
vsql -U doug -w password123 -c "select 1 c1"
vsql: FATAL 2248: Authentication failed for username "doug"

But this works:
vsql -U doug -w password123 -h sandbox1 -c "select 1 c1"

c1

1
(1 row)

Thanks Doug, yes, I do have authentication (local_hash) assigned to these users. I tried your method and yes, it worked when I passed the host name. Appreciate the help!

When you create a single authentication method, the intent is to lock things down.
See: https://www.vertica.com/blog/authentication-methods-dbadmin