Lytic Viruses -- Cell lysis?
Yes, ruptured here means that the host cell is destroyed. The virus "hijacks" the cell anyway and uses its protein production machinery to make as much virus particles and its transcription enzymes to makes as many viral genomes as possible. If the ressources of the cell are exhausted, it get destroyed and the viruses are set free.

See this image (from the Wikipedia article on the lytic process). It actually doesn't matter, if the virus infects the cell from the outside or if it comes from the genome.




Adsorption of the virus to the cell.
Injection of its genetic material into the cell.
Production of new viruses (hull and genome).
Rupture of the cell and release of the viruses.