Basically, yes, but the more commonly found term for that construction is bilattice following Ginsburg who saw the need to construct more complicated ones than Belnap's FOUR.
As M. Fitting more intuitively explains the definition (which he actually narrows a bit, but with respect to FOUR that doesn't matter) and the construction scheme:
Definition: By an interlaced bilattice we mean a set B together
with two partial orderings, ⩽t and ⩽k, meeting the conditions:
- each of the two partial orderings gives B the structure
of a complete lattice (hence arbitrary meets and joins
exist with respect to each ordering);
- the meet and join operation for each partial ordering is
monotone with respect to the other ordering.
[...]
There is a general and intuitively appealing method for constructing interlaced bilattices, due to Ginsberg. We describe it briefly.
Suppose C = (C, ⩽) and D = (D, ⩽) are complete lattices. (We
use the same notation, ⩽, for both orderings, since context can determine
which is meant.) Form the cartesian product C x D, and give it
two orderings, ⩽t and ⩽k, as follows.
- (c1, d1) ⩽k (c2, d2) if c1 ⩽ c2 and d1 ⩽ d2
- (c1, d1) ⩽t (c2, d2) if c1 ⩽ c2 and d2 ⩽ d1
The intuition here is rather nice. Suppose we think of a pair (c, d)
in C x D as codifying two independent judgements concerning the
‘truth’ of some sentence: c represents our degree of belief in it, while d
represents our degree of belief against it. Since C and D can be different
lattices, expressions of belief for and against need not be
measured in the same way.
If (c1, d1) ⩽k (c2, d2) then (c2, d2) embodies more ‘knowledge’ than (c1, d1), which is reflected by an increased degree of belief both for and against. On the other hand, if (c1, d1) ⩽t (c2, d2) then (c2, d2) embodies more ‘truth’ than
(c1, d1), which is reflected by an increased degree of belief for, and a decreased degree of belief against.
It's easy to see how FOUR is constructed that way from two copies of the two-element Boolean algebra 2, although the two copies have different (i.e. opposite) meanings assigned to their ⊥ and ⊤, as noted in that para.
The SEP article manages to make this construction slightly unclear because
it flips the symbols of one of boolean algebras... which is fine by isomorphism and probably intended from the viewpoint of
the "natural reading" of the output of the construction, but a wee bit confusing otherwise from the point of view of the construction.
Following the notation from Fitting, in the k-order the greatest element should be (⊤C, ⊤D) and in the t-ordering it should be (⊤C, ⊥D) obviously.
The SEP page basically has this notation/identification in its diagrams: ⊤ = ⊤C = ⊥D and ⊥ = ⊥C = ⊤D, so instead of (⊤C, ⊤D) SEP writes {⊤, ⊥} and instead of (⊤C, ⊥D) SEP simply writes {⊤}. And perhaps the most confusing part is that SEP writes ∅ for (⊥C, ⊥D). Or more helpfully, I hope, as a "double Hasse" diagram with the SEP notation on the right-hand side of each node's label:

For an (intuitionistic) example where C and D are not the same, Fitting uses the open and closed sets of a topological space.
The difference between SEP/Gottwald's (k-tuples) product systems and (interlaced) bilattice as defined above is basically that Gottwald's construction doesn't include taking the inverse ordering on one of the lattices as part of his definition. That actually makes Gottwald's construction more general than interlaced bilattices, but he doesn't given any examples for k>2, so it's not clear if anyone found a use/application for those.
Ginsburg himself defined bilattice somewhat more generally, which allows some examples that aren't strict interlacingins like that. Basically, besides two (starting) complete lattice (instead of Fitting's condition 2) he introduces a negation (on the bilattice) that is defined as having the properties that
- ¬¬ x = x and
- ¬ is a lattice homomorphism from C to C itself and from D to Dop (i.e. the lattice obtained from D by reversing its order).
Because of this you can have different number of elements (in both dimensions) on the chains in the resulting "product" in Ginsberg's construction, e.g.

Ginsberg used the term "world-based" to refer to the construction that Fitting later called interlaced bilatices. Ginsberg also defines a notion of a balanced bilattice which is called so if there is a surjective bilattice homomorphism from a world-based bilattice (construction) to it. The bilattice in the figure above is not balanced (unlike FOUR).