Entitlement to Payment
If he worked for you, even if it was for 5 days, he is entitled to payment, irrespective of whether he signed the offer letter or whether you gave him an appointment letter. The offer letter is an offer, his joining the training is acceptance, and your letting him join is evidence that the employment contract was honored. Your failure to issue an appointment letter is actually immaterial, except that by not giving it, you basically have fewer rights. You cannot enforce the notice period or terms of employment as you never communicated it to him. On the other hand, he is entitled to claim all standard terms and what is in Standing Orders (your certified one or model standing orders) as you didn't communicate otherwise.
Traveling Cost Entitlement
Whether he is entitled to traveling cost depends on the terms of the appointment (which you didn't sign or communicate). But if you asked him to travel to your office, then you are liable to pay for the travel. Only if you had very clearly stated that he will not be given travel cost for training, then he may not be entitled to it.
Offer Letter Withdrawal
You cannot withdraw an offer letter that is accepted. At best, you can issue a show cause (which you probably didn't), give him a chance to explain himself, issue a suspension (for which period also you have to pay 50% salary), and then conduct a domestic inquiry. If the inquiry officer finds it was misconduct, he can recommend punishment (which can include termination, and the recommendation should be justified). You can then act on it.
So frankly, if he is just asking for 7 days' salary and travel cost, it is much less than your cost otherwise.
Questionable Conduct
By the way, I am surprised someone can be so drunk as to miss work for 2 days on account of the same. Was the drink given by the company (like in a party, etc.)? Was being drunk the real reason or was there something else?