I see some really broad indemnification clauses in EULAs. Here's one from the Tower of Fantasy EULA:
You agree to indemnify (in other words, compensate for all and any losses incurred), pay the defense costs of, and hold the Company Parties and their employees, officers, directors, agents, contractors, and other representatives harmless from all claims, demands, actions, losses, liabilities, costs and expenses (including, without limitation, attorneys’ fees, costs, and expert witnesses’ fees) that arise out of or in any way are connected with: (a) your access to or use of the Services; or (b) any claim that, if true, would constitute a breach by you of this EULA. You agree to reimburse us for any payments made or loss suffered by us, whether in a court judgment or settlement, based on any matter covered by this Section 20.
As written, this indemnification clause does not explicitly restrict itself to third-party claims, or to claims over something that's the user's fault.
If I were to play this video game, almost anything I might want to sue this company over (or go to arbitration over, since there's an arbitration clause too) would be reasonably described as
connected with: (a) your access to or use of the Services
Even if I'm totally innocent and I'm trying to get compensation for something the company did wrong, anything wrong they did to me would almost certainly be connected to my use of the services.
Would that mean the indemnification clause applies?
Note that while the line preceding the quoted paragraph,
If someone sues us based on your breach of this EULA or your access or use of the Services, you agree to defend us or pay for our defense in that lawsuit.
might seem to limit the indemnification clause, that line is not actually part of the EULA. Quoting section 2 of the EULA,
You’ll notice that we added some text in italics throughout the EULA to make it easier to read; however, this text is provided for guidance only, and does not form part of the EULA.
That line is italicized, so not part of the EULA.