The phraseology was slightly incorrect, this is from the FAA's ATC Orders (section 3-10-5):

3−10−5. LANDING CLEARANCE
a. When issuing a clearance to land, first state the runway number followed by the landing clearance. If the landing runway is changed, controllers must preface the landing clearance with “Change to runway.”
PHRASEOLOGY−
RUNWAY (number) CLEARED TO LAND.
Or
CHANGE TO RUNWAY (number) CLEARED TO LAND

That means the ATC instruction should have been:

American 2293 Heavy, change to runway 28L, cleared to land

All the correct information was in the transmission you quoted, it was just given slightly out of order. But that could easily be an issue for a pilot who's in a high-workload phase of flight and it's probably exactly why the ATC orders say that the words "change to runway" must come first.

I've had ATC change my landing clearance a couple of times but the controller always asked me first if I could do it:

Tower: N12345, cleared to land 21L
N12345: Cleared to land 21L, N12345
[A few seconds later...]
Tower: N12345, are you able to switch to 21R?
N12345: Affirm, we can do that, N12345
Tower: N12345, change to runway 21R, cleared to land

However, landing a C182 at a class D is a bit different from landing a heavy at SFO; I assume the controllers there have less time to talk so they may simply have changed the clearance and expected the pilot to say "unable" if necessary.

The phraseology in the video was slightly incorrect at the time it was issued. Due to further clarifications, that phraseology is now even more of a departure from the current guidance.

When that video was posted in April 2015, the current version of the ATC Order was FAA JO 7110.65V, Change 2. Paragraph 3–10–5 prescribes the "change runway" phraseology, and that paragraph was not modified in Change 2 nor in Change 1; thus the paragraph published in JO 7110.65V "basic" was in effect:

3−10−5. LANDING CLEARANCE
a. When issuing a clearance to land, first state the runway number followed by the landing clearance. If the landing runway is changed, controllers must preface the landing clearance with “Change to runway.”
PHRASEOLOGY−
RUNWAY (number) CLEARED TO LAND.
Or
CHANGE TO RUNWAY (number) CLEARED TO LAND

That means the ATC instruction should have been:

American 2293 Heavy, change to runway 28L, cleared to land

All the correct information was in the transmission you quoted, it was just given slightly out of order. But that could easily be an issue for a pilot who's in a high-workload phase of flight and it's probably exactly why the ATC orders say that the words "change to runway" must come first.

Paragraph 3–10–5 was modified by Notice N JO 7110.761 dated October 26, 2018:

3-10-5. LANDING CLEARANCE
a. When issuing a clearance to land, first state the runway number followed by landing clearance. If the landing runway is changed, controllers must preface the landing clearance with “Change to runway” followed by the runway number. Controllers must then restate the runway number followed by the landing clearance.
PHRASEOLOGY-
RUNWAY (number) CLEARED TO LAND
Or
CHANGE TO RUNWAY (number), RUNWAY (number) CLEARED TO LAND.
NOTE-
The purpose of the ‘change to runway’ phraseology and restating the runway number is to emphasize to the pilot that they are being cleared to land on a runway other than what they were expecting.

The background information in the change notice says that "This new language builds on previous mitigations and is intended to clarify the "runway" on which a pilot is to land."

N JO 7110.761 was incorporated into JO 7110.65X, Change 3, dated February 28, 2019.

I've had ATC change my landing clearance a couple of times but the controller always asked me first if I could do it:

Tower: N12345, cleared to land 21L
N12345: Cleared to land 21L, N12345
[A few seconds later...]
Tower: N12345, are you able to switch to 21R?
N12345: Affirm, we can do that, N12345
Tower: N12345, change to runway 21R, cleared to land

However, landing a C182 at a Class D is a bit different from landing a heavy at SFO; I assume the controllers there have less time to talk so they may simply have changed the clearance and expected the pilot to say "unable" if necessary.