Yes, if the actual duties fit a listed profession such as Computer Systems Analyst and the employer describes them accurately. The letter should identify the claimed profession, but the job title need not reproduce the Appendix label verbatim; the work must genuinely be that profession's work.
The list names professions, not job titles
Appendix 2 does not contain software developer or programmer, and its Engineer category does not cover every position that technology employers call engineering. It does contain Computer Systems Analyst, and some development roles may fit when their actual primary duties involve requirements analysis, system design and specification. The test is what the applicant will do, not what the industry calls the job.
An offer with duties limited to writing code is a poor fit; duties centred on analysing business needs, designing solutions and specifying them may fit Computer Systems Analyst even if coding is incidental, provided that description is true. The Paradise developer's prior systems work can help document relevant experience. Engineer is a separate profession requiring the specified engineering degree or licence, and a computer-science diploma does not satisfy that credential rule.
Get the claimed profession and the duties right before signing, not merely the title.