Log Horizon‘s third season doesn’t waste any time with recaps, so it’d be best if you re-watched the earlier episodes before jumping in. Doing so will also prepare you for it’s somewhat unconventional mix of actionless dialog-heavy arcs and action-focused arcs.
Back when I first saw the series the only MMO I had played was City of Villains, but now after getting involved with FFXIV I can actually appreciate the extensive mechanic-related references. So experience with the subject matter will definitely influence your enjoyment level… but at the end of the day the choice of whether or not to watch it comes down to how much tolerance you have for extraneous exposition.
Horimiya meanwhile is an alternate version of an OVA series which fully adapts their shared source material in record time. Which isn’t a complement. This is the kind of story that wants to breath, and here it’s never given the chance.
Oh the comedy is certainly good and it’s nice to have a cast of characters who actually talk to each other about their problems rather than let misunderstandings fester, but everything develops at such a breakneck pace it strains credulity. It crams over a year of its characters lives and relationship developments into a mere 13 episodes. Just because the show tells you (indirectly) that a month has passed in a second doesn’t make accepting it any easier.