A request with no version number is a HTTP/0.9 request, also known as a "simple-request". If supported, it will receive a much simpler response than a HTTP/1.0 or later request.
RFC 1945, (the HTTP/1.0 specification) includes the definition for such requests (see section 5) and requires servers to support them, but discourages their use by clients.
RFC 2068 and RFC 2616 (the original and first revised version of the HTTP/1.1 specification) no longer includes the definition for such requests. They say that "It is beyond the scope of a protocol specification to mandate compliance with previous versions." but that "at the time of composing this specification" they would expect "commercial web servers" to continue supporting http/0.9 and http/1.0.
When http/1.1 was again revised in 2014, it was split into a series of RFCs (RFC 7230 to 7235) rather than one large document. RFC 7230 reccomends that servers that support name based virtual hosting do not support http/0.9 requests.
Are webservers meant to honor this HTTP/0.9 request?
The internet is built on "rough consensus and running code". The IETF does it's best to document that consensus and make recommendations, but ultimately what level of backwards compatibility to offer is a judgement call for individual implementers.
Practically speaking, the modern web is heavily reliant on name based virtual hosting. Therefore even if the web server software understands such ancient requests there is a good chance it will not return the desired document,