score:3
Business or tourism are not clearly defined categories with a separate list of formal requirements. The key requirement behind all this is having a legitimate and plausible purpose for the trip. So you simply need to provide documentation that makes sense and supports your plans.
Clearly, you are not going there for tourism so “business” makes more sense. The reason why they ask a letter from your current employer is that they assume that most business trips will be on behalf of that employer (think visiting clients, attending a training paid by the employer, etc.) But applying without it should be fine in this case. If you are still uneasy about “business”, you could also check “other” and write “job interview”.
Regarding your leave, I am not 100% sure of the way this works in India. Any sort of proof that your employer approves your absence would clearly be useful but do you need to be completely upfront with them about the purpose of the trip?