The case which you have talked about is certainly relating to 'Issue of shares on Preferential basis' and not of a 'Rights Issue'.
For understanding the reason behind this, let me explain you below concepts clearly :
(1) Issue of shares on Preferential basis :
In certain situations, it may not be desirable to issue shares to the public at large. Since issuing shares to the public is a very detailed and expensive excercise. It may be avoided where the issue size is small which can be fully subscribed by the directors and existing shareholders. This is called as 'Issue of shares on preferential basis'.
(2) Issue of shares on Private Placement basis :
When issue size exceeds the resources that can be raised from directors and existing shareholders, there is a possibility of 'placing' shares 'privately' with friends, associates, financial Institutions, mutual funds etc. This is called as 'Issue of shares on private placement basis'
(3) Rights Issue :
Shares offered to all existing shareholders of a company is called as 'Rights Issue'. In the rights shares, the shareholders of a company have a pre-emptive right to subscribe to these shares. (Please note that a director may or may not be a shareholder. If he is not a shareholder, the rights shares would not be offered to him.)
(4) Public Issue :
Offer or invitation to subscribe for shares or debentures made by companies to 50 persons or more will be treated as 'public issue'.
Procedure for preferential allotment :
1. Hold a Board meeting. In that meeting, fix the date of General Meeting to pass a Special Resolution under Section 81 (1A).
2. File e-Form 23 with ROC within 30 days of General Meeting Resolution.
3. After passing Special Resolution in General Meeting, hold another Board Meeting for allotment of equity shares.
4. File e-Form 2 within 30 days of Board Meeting allotment Resolution.
Please note that, an unlisted public company has to follow 'Unlisted Public Companies (Preferential Allotment) Rules, 2003' while making the above allotment of shares and MCA is contemplating to introduce more stringent rules by name 'Unlisted Public Companies (Prefrential Allotment) Amendment Rules, 2011'. So, I advise you to complete the allotment as soon as possible.
For your reference, I have attached, Unlisted Public Companies (Preferential Allotment) Rules, 2003 with this reply. Please find the same.