TVs cannot record video. I have absolutely no idea what you are talking about.
A VHS ("tape") machine records video in analogue on a thin magnetic film. This means that there is no concept of pixels and instead an image is reconstructed using Analogue to Digital converters (where this happens depends on wiring, usually in the TV as the VHS machine outputs on SCART or other kinds of analogue connector).
A DVD recorder does write digital data. However since DVD is SD it has to do very little work. It also has highly optimized hardware for encoding which can include purpose built integrated circuits and processors.
Blu-ray recorders work in a similar way to DVD recorders but "cranked up to 11". Basically they will have considerably more powerful integrated circuits and processors to manage encoding. This is obvious as HD will use >4 times the processing power over SD.
Smart set-top boxes such as offered by Virgin Media, Sky and Freesat simply use a weaker encoder as they have more space available to them. That is if they can record in HD (at one stage Sky offered a different special box to do that but I think all of them do this by standard now). Again it is probably aided with special purpose hardware and since they all their input sources are already encoded digital it likely can re-encode considerably faster (how it can record multiple channels in HD at once).
Both the Xbox One and Sony PlayStation 4 have dedicated system resources for their live video capture. Specifically about 1/4 of the console processing power and 1/2 of the console memory is dedicated to this although I think they cut that back a bit due to people complaining of poor performance for something brand new.
Modern PC systems which use new NVidia graphic accelerators can use NVidia's GPU video capture system that is part of their GeForce experience drivers. As this mostly uses the GPU for encoding (GPUs are good at that kind of operation) it performs very well and can easily capture HD streams on any decent gaming card without heavily loading the CPU.
Laptops are not designed for video capture. Not only do they have weak GPUs (most probably struggle to run the game, those that do not will certainly struggle with GPU accelerated video capture) but also are highly prone to overheating. Their CPUs are not designed for running at full power continuously as they are built with insufficient cooling. If integrated graphics are used you are limited by fill rate (which video capture uses a lot of) since the main memory is being used by both the CPU (game logic) and the graphics (which needs a lot of memory read/write).
What I don't understand is that my laptop is powerful enough to run Warcraft 3 to 2 monitors on full resolutions and graphics, while it struggles to record. Why doesn't Hypercam just duplicate the signal? What am I missing?
Because a full 1080p HD stream running at 30 FPS when uncompressed consumes 249 MB/sec. 60 FPS? That is 500 MB/sec (or 30 GB/min). As such it has to compress the generated images, preferably with lossy compression, so that the amount of data can be realistically stored. However it still needs to process 250/500 MB/sec worth of image data using computationally expensive algorithms which is why your laptop is struggling. It might even be saturating main memory I/O bandwidth since that is only in the order of a few GB/sec. Reducing to SD works as instead of 250 MB/sec it is only 62.5 MB/sec odd, a
huge reduction.
2nd Gen Quad Core Intel i7 2Ghz
Low clock speed which is bad for such computationally intensive tasks. Also probably only runs at 1 GHz on average due to overheating.
Poor fillrate, sub gaming power, oldish (3 years). Probably also will overheat and slow down if used at full power. To put it in perspective it is about as powerful as what the PS3 used and that had very few full HD games.
Well SSDs do not have the cappacity of HDDs
Incorrect. They do not have the
affordable capacity of mechanical HDDs however they have physical capacity on par. I know this as I just installed a 1TB SDD laptop hard disk for someone which is approximately 1/4 or less of the size of a conventional desktop mechanical drive. It can
read and write simultaneously at >200 MB/sec. It did cost like £400 odd so not very affordable when £50 odd nets you several TB of mechanical drive storage.