[Serve.llm] remove old vllm+serve doc (#51311)

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## Why are these changes needed?

Remove old vllm+serve doc so people are not confused with the new
serve.llm apis.

## Related issue number

<!-- For example: "Closes #1234" -->

## Checks

- [ ] I've signed off every commit(by using the -s flag, i.e., `git
commit -s`) in this PR.
- [ ] I've run `scripts/format.sh` to lint the changes in this PR.
- [ ] I've included any doc changes needed for
https://docs.ray.io/en/master/.
- [ ] I've added any new APIs to the API Reference. For example, if I
added a
method in Tune, I've added it in `doc/source/tune/api/` under the
           corresponding `.rst` file.
- [ ] I've made sure the tests are passing. Note that there might be a
few flaky tests, see the recent failures at https://flakey-tests.ray.io/
- Testing Strategy
   - [ ] Unit tests
   - [ ] Release tests
   - [ ] This PR is not tested :(

Signed-off-by: Gene Su <e870252314@gmail.com>

Author: GeneDer

doc/BUILD

@@ -222,7 +222,6 @@ py_test_run_all_subdirectory(
         "source/serve/doc_code/intel_gaudi_inference_client.py",
         "source/serve/doc_code/distilbert.py",
         "source/serve/doc_code/stable_diffusion.py",
-        "source/serve/doc_code/vllm_openai_example.py",
         "source/serve/doc_code/object_detection.py",
         "source/serve/doc_code/http_guide/streaming_example.py",
         "source/serve/doc_code/http_guide/websockets_example.py",

doc/source/cluster/kubernetes/examples/vllm-rayservice.md

@@ -2,7 +2,7 @@
 
 # Serve a Large Language Model with vLLM on Kubernetes
 
-This guide demonstrates how to [Serve a Large Language Model with vLLM](https://docs.ray.io/en/latest/serve/tutorials/vllm-example.html) on Kubernetes using KubeRay. The example in this guide deploys the `meta-llama/Meta-Llama-3-8B-Instruct` model from Hugging Face on Google Kubernetes Engine (GKE).
+This guide demonstrates how to Serve a Large Language Model with vLLM on Kubernetes using KubeRay. The example in this guide deploys the `meta-llama/Meta-Llama-3-8B-Instruct` model from Hugging Face on Google Kubernetes Engine (GKE).
 
 ## Prerequisites
 

doc/source/serve/doc_code/vllm_openai_example.py

@@ -16,14 +16,6 @@ examples:
       - generative ai
     link: tutorials/stable-diffusion
     related_technology: ml applications
-  - title: Serve a Large Language Model (LLM)
-    skill_level: beginner
-    use_cases:
-      - generative ai
-      - large language models
-      - natural language processing
-    link: tutorials/vllm-example
-    related_technology: ml applications
   - title: Serve a Text Classification Model
     skill_level: beginner
     use_cases: