A simple way is to point a camera, such as a smartphone camera, at the TV screen to record.
Hello, as Diablo is a modded series, you can request a new leaderboard by messaging the mods at the bottom of the series page.
https://www.speedrun.com/diablo_series#platform=&orderby=oldest&unofficial=on
Yes, you can find individual levels by selecting the “level leaderboard” drop down under leaderboards. Here is the link to 2-5 on Wii U:
https://www.speedrun.com/sm3dw/level/World_2?h=Normal-2-5&x=l_gdryj2lw-8240l6wd-p854yevl.81wwok51
And here it is on Switch:
https://www.speedrun.com/sm3dw_bf/level/World_2?h=Normal-2-5&x=l_nwl4k3r9-ndx5qe1k-38dpogx8.21d96n3q
If your computer isn’t powerful enough to run both the game and OBS, you could point an external camera at the screen and record with that instead.
Pick a category, read the rules for the category, record yourself playing with either a camera on the screen or a capture card, upload the video somewhere, then submit.
https://www.speedrun.com/mk8?h=32_Tracks-150cc&x=xd1m7rd8-ylpm6vlg.p12z6d1x