The section of Tax Topic 413 you are looking at is titled "IRA-to-IRA Rollover Limitation" and applies only to movement of funds from traditional IRA to traditional IRA and Roth IRA to Roth IRA. IRS Revenue Ruling 78-406 provides the basis for the term "trustee-to-trustee transfer."
Movement of funds from an IRA to a 401(k) , 403(b) or 457(b) is relatively uncommon compared to movement of funds in the other direction, so it's not surprising that references mostly mention rollovers from employer plans. Yes, a 457(b) is an employer plan.
The difference between IRAs and employer plans that leads to this distinction is that an employer plan is self-contained and independent of other employer plans and IRAs, while, unlike employer plans, multiple IRA's of an participant are treated as a single account for most purposes. Since the IRAs are treated as a single account, transferring funds from one IRA to another with no payment made to any entity other than the receiving IRA is treated the same as an investment change within a particular IRA account.
You can experiment with the Interactive Tax Assistant provided by the IRS:
https://www.irs.gov/help/ita/do-i-need-to-report-the-transfer-or-rollover-of-an-ira-or-retirement-pl...
