I don't have Apache web server. Can I use some other web server?

Yes. You can use any web-server you want. Videocache requires your web-server to alias /var/spool/videocache/ directory as /videocache/ so that it can be accessed via http://your_system/videocache/ . If you have a web server that supports aliasing, you can use it without any worries. Check this tutorial for videocache with lighttpd.