Synchronized video playback over the network
After looking for a similar solution myself (synchronized playback with files on both computers, no streaming nor multicast), I found several solutions, most being free and some being opensource.
Desktop applications
The following applications must be installed on both computers to allow synchronized playback:
SyncPlay: opensource software to synchronize playback of videos and/or audio files. The synchronization packets will pass through the SyncPlay servers, but the software is opensource so you can make your own master server if you want. Crossplatform and works with several different players, like mpv or VLC (v2 natively supported in latest SyncPlay, before you had to install the additional VLC-syncplay plugin -- for VLC v3 there is an issue that will get resolved in the future). SyncPlay itself is quite easy to use: just launch SyncPlay and choose a (IRC-like) server, a room name and a file to sync and it will launch your video player with everything needed. You can then tell your friends to choose the same server, room name and file to be synchronized. A full log will show everyone's actions in realtime.
RiftMax Theater is a media player that is specifically made to synchronize playback.
Virtual Reality Theaters, like VRTV Free and similar Cardboard/Occulus virtual reality apps: if both of you have a virtual headset, the "virtual theater" apps usually offer synchronized playback over internet with users of the same headset.
Web-based apps
These applications run in the browser but they allow to use your own files:
- Gaze
- Synaptop
http://www.mplayerhq.hu/DOCS/HTML/en/networksync.html
Seems that mplayer lets you sync video over the network.