curl fails to retrieve HTTPS content: error:14094410:SSL routines:ssl3_read_bytes:sslv3 alert handshake failure

I believe there are actually two somewhat overlapping problems here, both related to the server apparently being way out of date or else insanely operated. Analysis by ssllabs shows it supports only SSLv3 and TLSv1.0 protocols, and only four ciphersuites:

TLS_RSA_WITH_RC4_128_MD5 (0x4)   INSECURE   128
TLS_RSA_WITH_RC4_128_SHA (0x5)   INSECURE   128

(which in the OpenSSL naming scheme are DES-CBC-SHA, DES-CBC3-SHA, RC4-MD5 and RC4-SHA).

First, as noted by SSLLabs the server is "version intolerant"; if you send it ClientHello offering versions above 1.0 in a record with version 1.0 (and otherwise acceptable) it negotiates down to 1.0 as it should*, but if you send this offer with record version 1.1 or 1.2, as some software does (but not AFAICT any recent OpenSSL), the server aborts with alert close_notify (which is not correct for this state). (*: well, as it should given that it's supporting 1.0 at all)

Second, it supports only the four ciphersuites above. Very recent versions of OpenSSL and specifically 1.1.0g no longer support single-DES (at all) because it is completely broken, and do not support RC4 or triple-DES by default because of various biases and the generic birthday attack; thus if OpenSSL is used there are no ciphersuites in common and the server correctly aborts with alert handshake_failure. But it should be possible to enable RC4 and/or TDES, unless they were configured out at build (compile) time. I notice your Windows version shows (WinSSL) in addition to OpenSSL/1.1.0g; I don't know if this means schannel is used here (or at all), in which case it might be the reason --ciphers RC4-SHA (using the OpenSSL naming scheme) didn't work.

Note on Windows programs, especially 'imports' like curl and OpenSSL, typically don't share libraries as they do on Unbuntu and most Linux (and other Unix). You might try openssl version on your Windows OpenSSL to see which it is; I'll bet it's not the latest and if you get the latest it will exhibit the same issue from commandline.

Ubuntu 16.04 (I assume LTS?) is not bleeding edge and it makes sense for it to still support ciphers that were deprecated only recently.