Does excess damage (with VII for example) need a surviving unit on the battlefield on the opposite side?

No. Excess damage does not require a surviving enemy unit.

Excess damage is calculated during the Combat Damage Step as part of assigning damage — before any units actually die. You assign lethal damage to each defending unit in order, and any leftover damage assigned to the last defending unit beyond what's needed to kill it is excess (Rule 460.2.c.3–4, FAQ #67). The units then die from that damage afterward, but the excess was already set.

For example, if you swing with 5 total Might at a single 2-Might defender, you assign all 5 to it (it's the only unit left), and you've assigned 3 excess damage — even though that defender won't survive (FAQ #11558). Piltover Enforcer's "3 or more excess damage" trigger works just fine.