His idea can be seen from the first three (of six) Chapters in his "Contents". In particular in Chapter II.3 he defines his normal algorithm (see sub-section below) in terms of a set of symbols that form words, and a method using substitution rules to create new but valid words.

Although this sounds exactly like a "recursive language" ("Equivalence of a type 0 grammar to a Turing Machine" cf Hopcroft and Ullman p. 221, Introduction to Automata theory, Languages and Computation, Addison-Wesley, 1979) nowhere do Hopcroft and Ullman cite Markov, neither in their index nor in their bibliography.  

Chapter I. LETTERS, ALPHABETS, WORDS
 1. Letters
 2. Alphabets
 3. Words
 4. Entries
 5. Links and chains
 6. Translations

Chapter II. THE NOTION OF ALGORITHM
 1. Algorithms in alphabets
 2. Examples of algorithms
 3. Normal algorithms
 4. Examples of normal algorithms
 5. The principle of normalization

Chapter III. CONSTRUCTION OF NORMAL ALGORITHMS
 1. Extension of an algorithm
 2. Closure of an algorithm
 3. Composition of algorithms
 4. Combination of algorithms
 5. Branching of algorithms
 6. Reiteration of algorithms
 7. Translation of an algorithm
 8. Some algorithms connected with matrices

 Nutshell description of Markov's definition of his "normal algorithm" (pp.63ff) 

In particular, the notion "2." of "steps of local nature" appear also in Blass and Gurevich with regards to Kolmogorov-Uspensky (KU) machines:
Gurevich proposed to Uspensky that " 'every computation, performing only one restricted local action at a time, can be viewed as (not only  being simulated by, but actually being) the computation of an appropriate KU machine.' Uspensky concurred." (Blass, Gurevich 2003, p. 10)

Markov's definition:  

"1. Separate elementary steps, each of which will be performed according to one of these rules..."

"2. ...steps of local nature ..." [as opposed to "integral nature" ... he means that the algorithm won't change more than a certain number of symbols to the left or right of the observed word/symbol ]

"3. Rules for the substitution formulas ..."
 1) order given is their preferred order of use
 2) apply substitution to the first entry of the left-hand member

"4. Definite prescription for termination..."
 1) a means to distinguish a "concluding substitution"
 2) "simple"

"5. [He defines the above as a "normal algorithm"]

"6. [the "scheme" of the algorithm is the list of the substitution rules.]