tools: fix nits in tools/doc/type-parser.js

Checklist

• make -j4 test (UNIX), or vcbuild test (Windows) passes
• commit message follows commit guidelines

Style nits:

• Remove redundant variable.
• Rename and regroup variables for consistency.
• Rearrange export to reduce indentation level (unnecessarily increases diff, unfortunately).
• Replace common function by arrow function in .forEach() argument.
• Replace .indexOf() with .includes().
• Unify string concatenation, replace with template strings.

HTML nit:

• Remove extra line break in the output (reduces overall docs size by 78 KB).

Logic nit:

• Throw when type slot is empty (on things like { }, { | type }, { type | }).