FFplay (part of FFmpeg), mpv and MPlayer will seek very fast over .ts, without any pre-processing required. Use the arrow keys and PGUP/PGDN to navigate, with FFplay you can also right-click on the playing video to seek to that position - video width represents % of the video. When navigating .ts you may observe slow-motion-like effect (FFplay) or slight offsync (MPlayer), but those will stabilize in a few seconds. Nothing of that kind was observed with mpv, it is very robust and always exact.
You can get them all for different platforms. Your question indicates Windows, so for FFplay you can try Windows builds by Zeranoe, mpv has everything on their page, and for MPlayer check the updated Windows builds. Best overall seems to be mpv, it has many advanced options and features, including D3D11 and Vulkan support.
Another great and free choice is SMPlayer, which is a GUI front-end for MPlayer and mpv. You can switch between one or another engine under preferences, both will offer fast seeking with .ts files, and much more.
Optional: When a more universal solution is required, .ts must be remuxed into some other format, like .mkv - it offers fast seeking and similar resilience on top of file size reduction. With FFmpeg it can be done without re-encoding, like this:
ffmpeg -i "video 01.ts" -c copy "video 01.mkv"
I'd want something even better and more minimalist, ideally the removal of the top bar to maximize display space.
As a comment, I don't believe that removing the title bar increases the video size in any way. That said, you can achieve the removal of the window title bar with some of the command line options for VLC.
Borderless
To remove all the window elements from VLC, you will likely want to use the --no-video-deco and --no-embedded-video command line options:
vlc --no-video-deco --no-embedded-video example.mp4
Note that --no-video-deco and --no-embedded-video will likely only have a noticeable effect when a media source is specified (ex. example.mp4).
Be aware that using these options may remove the ability to move the window with click/hold/drag.
Placement
You can use the --video-x and --video-y options respectively to specify where you want your playback window to initially appear (starting from the uppermost left corner of the screen):
vlc --video-x=100 --video-y=100 --no-video-deco --no-embedded-video example.mp4
Size
If you want to change the size of the video, you can adjust the --zoom factor of the video:
vlc --zoom 2 --video-x=100 --video-y=100 --no-video-deco --no-embedded-video example.mp4
--zoom can take whole as well as decimal numbers (e.g. 0.25, 1.5, 2, etc.).
A --zoom under one reduces video size and a --zoom over one enlarges it.
If there's a method to achieve this for streaming sites like youtube I'd be interested as well.
example.mp4 is used as a video source above, but this could be e.g. a YouTube URL as well:
vlc --no-video-deco --no-embedded-video https://www.youtube.com/watch?v=qnEMOQTh27s
Caveats
Windows
Using --no-video-deco and --no-embedded-video with vlc will create two VLC windows — a "main" window with all the normal controls and separate borderless "playback" window. You can automatically minimize the "main" window by using the Windows start command with VLC i.e.:
start "" /min vlc --no-video-deco --no-embedded-video example.mp4
Any borderless playback window for a source started from the command line will close automatically once the file is finished.
The path to vlc needs to be in your environment variables to use vlc at the command line. Otherwise, you will likely need to specify the full path to vlc.exe in your commands.
Streaming
One thing to keep in mind about streaming sites in general (and YouTube in particular) is that there are multiple ways to stream data. For instance, the example YouTube link above (https://www.youtube.com/watch?v=qnEMOQTh27s) works in VLC. However, the one below (https://www.youtube.com/watch?v=4o0r9unT4L4) does not:
vlc --no-video-deco --no-embedded-video https://www.youtube.com/watch?v=4o0r9unT4L4
In cases like this, you might have to find alternative software such as mpv combined with youtube-dl if you really want to watch a given stream.
Sources
Best Answer
I have tried the example video on a fast computer with a high-level NVIDIA card.
I have downloaded both MP4 versions : "High Quality (fast GPU)" and "Low Quality (slower GPU)". I use the K-Lite Mega Codec Pack.
Playing the High Quality version, the results were very good and almost identical with either Windows Media Player, VLC or MPC-HC.
However, playing the Low Quality version was impossible with Windows Media Player because of high pixelation and stuck video. The results were however good with VLC and MPC-HC.
I hazard two conclusions :
The Low Quality version is badly encoded in such a way that makes its playing impossible, at least with Windows Media Player (which uses K-Lite, while the others use mostly codecs that come packaged with them).
Your computer specs may not be up to playing such videos at that speed, and this can be either because of the video card, memory, the bus, the disk, or even all of them.
In the second case, using a good video converter may convert the videos to something you can watch.
Try and see how you can play the High Quality version (life is full of surprises).