In Jainism, bondage (bandha) of karma is not limited to humans alone. It happens in every realm where a jiva (soul) exists, including the tiryanch (animals, insects, etc.) and even the higher and lower realms. The key idea is that karmic particles cling to the soul due to wrong belief, passions, and improper conduct, and this influx (āsrava) and binding (bandha) can occur in any realm where the soul is conscious enough to attract karma.

How this works across realms:

• The eight kinds of nature-bondage (prakṛtibandha) describe how karma binds the soul in all existences. The binders include: knowledge-obscuring (jñānāvaraṇa), perception-obscuring (darśanāvaraṇa), feeling-producing (vedanīya), deluding (mohanīya), life-determining (āyuḥ), name-determining (nāma), status-determining (gotra), and obstructive (antarāya) karma. These binders can operate no matter which gati (realm) the soul currently inhabits. ( wisdomlib.org)
• The inflow (āsrava) of karmas occurs through actions, thoughts, and passions. Deluding and other karmas trap the soul further, feeding both pain and pleasure experiences (vedaniya) in any realm. The result is bondage and the possibility of suffering (vedanā) and delusion (mohanīya) no matter where the soul is. ( jainknowledge.com)
• The practical picture is: wherever the soul takes birth—humans, animals in tiryanch, or other realms—the same karmic system operates. The duration and type of karma fruit depend on the particular karma and the soul’s mental state, but the mechanism of āsrava and bandha is universal. ( jainknowledge.com)

On the idea that dharma is only in certain realms: in Jain thought, dharma (righteous conduct, right belief, and nonviolence) is an ideal path that helps prevent new karmas from inflowing and aids shedding existing karmas. It is not restricted to humans; following right faith, right knowledge, and right conduct is a universal path to reduce bondage, even for beings in tiryanch. The practice and its consequences are described consistently in the Jain karmic framework. ( jainknowledge.com)

If you’d like, you can read more about how karma bondage works in Jain texts here:

• You can read more about the eight kinds of nature-bondage here