Is an employee's taking money from a company considered rightfully seizing a right or theft, if the employer refuses to increase his salary or transfer his sponsorship, yet acknowledges his efficiency and prefers him over others in financial dealings?

It is not permissible to take anything from the company's funds without the owner's permission, as this is a breach of trust, and it does not fall under the category of "securing one's right" which requires the right to be established and the inability to obtain it through any other means. Your perception that you deserve a higher salary does not justify this breach of trust, as the determining factor is the contract between you and the employer. As Shaykh al-Islam Ibn Taymiyyah said: "It is not permissible for an employee to take more than what was stipulated for him under the pretext that he deserves more, for this is forbidden, whether the employer is a ruler, a governor, or an agent." If the employer does not agree to increase your salary, then you either remain and fulfill the trust, or you seek other employment.