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GH-37308: [C++][Docs] Change name for CPP tutorial and minor fixes to the job (#37311)

### Rationale for this change

Fix the job and rename so it's picked up as part of the nightlies

### What changes are included in this PR?

Rename + fixes to the job.

### Are these changes tested?

Via CI

### Are there any user-facing changes?

No
* Closes: #37308

Lead-authored-by: Raúl Cumplido <raulcumplido@gmail.com>
Co-authored-by: Sutou Kouhei <kou@cozmixng.org>
Signed-off-by: Sutou Kouhei <kou@clear-code.com>