Cardinality Estimation for >= and > for intra step statistics value
The only difficulty is in deciding how to handle the histogram step(s) partially covered by the query predicate interval. Whole histogram steps covered by the predicate range are trivial as noted in the question.
Legacy Cardinality Estimator
F = fraction (between 0 and 1) of the step range covered by the query predicate.
The basic idea is to use F (linear interpolation) to determine how many of the intra-step distinct values are covered by the predicate. Multiplying this result by the average number of rows per distinct value (assuming uniformity), and adding the step equal rows gives the cardinality estimate:

Cardinality = EQ_ROWS + (AVG_RANGE_ROWS * F * DISTINCT_RANGE_ROWS)

The same formula is used for &gt; and &gt;= in the legacy CE.
New Cardinality Estimator
The new CE modifies the previous algorithm slightly to differentiate between &gt; and &gt;=.
Taking &gt; first, the formula is:

Cardinality = EQ_ROWS + (AVG_RANGE_ROWS * (F * (DISTINCT_RANGE_ROWS - 1)))

For &gt;= it is:

Cardinality = EQ_ROWS + (AVG_RANGE_ROWS * ((F * (DISTINCT_RANGE_ROWS - 1)) + 1))

The + 1 reflects that when the comparison involves equality, a match is assumed (the inclusion assumption).
In the question example, F can be calculated as:
DECLARE 
    @Q datetime = '1999-10-13T10:48:38.550',
    @K1 datetime = '1999-10-13T10:47:38.550',
    @K2 datetime = '1999-10-13T10:51:19.317';

DECLARE
    @QR float = DATEDIFF(MILLISECOND, @Q, @K2), -- predicate range
    @SR float = DATEDIFF(MILLISECOND, @K1, @K2) -- whole step range

SELECT
    F = @QR / @SR;

The result is 0.728219019233034. Plugging that into the formula for &gt;= with the other known values:

Cardinality = EQ_ROWS + (AVG_RANGE_ROWS * ((F * (DISTINCT_RANGE_ROWS - 1)) + 1))
            = 16 + (16.1956 * ((0.728219019233034 * (409 - 1)) + 1))
            = 16 + (16.1956 * ((0.728219019233034 * 408) + 1))
            = 16 + (16.1956 * (297.113359847077872 + 1))
            = 16 + (16.1956 * 298.113359847077872)
            = 16 + 4828.1247307393343837632
            = 4844.1247307393343837632
            = 4844.12473073933 (to float precision)

This result agrees with the estimate of 4844.13 shown in the question.
The same query using the legacy CE (e.g. using trace flag 9481) should produce an estimate of:

Cardinality = EQ_ROWS + (AVG_RANGE_ROWS * F * DISTINCT_RANGE_ROWS)
            = 16 + (16.1956 * 0.728219019233034 * 409)
            = 16 + 4823.72307468722
            = 4839.72307468722

Note the estimate would be the same for &gt; and &gt;= using the legacy CE.