Final answer:
The main enzyme encoded by retroviruses, LTR-retrotransposons, and some non-LTR-retroposons is reverse transcriptase, which facilitates the reverse transcription of their RNA genome into DNA for integration into the host genome.
Step-by-step explanation:
The main enzymatic activity encoded by retroviruses, LTR-retrotransposons, and some non-LTR-retroposons is reverse transcriptase. This enzyme is essential for the replication of their genome. Retroviruses, like HIV, have an RNA genome that needs to be reverse transcribed into DNA, which is then integrated into the host's genome. The enzyme reverse transcriptase converts the viral RNA template into DNA, a process that does not occur in uninfected host cells and is exclusive to the presence of viral genes in the infected cells. This enzyme has been a target for the development of antiviral drugs that inhibit viral replication, such as the reverse transcriptase inhibitor AZT, without affecting the host's metabolism.