What is the meaning of "rage," in this exchange

Solution 1:

I'm not sure, but I think the relevant sense is probably this noun sense (from the Middle English Dictionary):

6. Amorous longing or desire, lovesickness; also, a fit of carnal lust or sexual desire; a feeling of passion or love; ~ of love, an ardent passion; loves ~, the fervor of love.

[link]

So I think the verse means something like, "I like both sex and desire" (plei meaning, among other things, "sex").

Solution 2:

Online Etymology has some interesting background for rage; until the mid-13c., it meant

"to play, romp," from rage (n.) [After that a new meaning was acquired:] Meanings "be furious; speak passionately; go mad" first recorded c. 1300.

So, it may be a repetition of play (as in "romp and play"), or it may be fight/go mad/whatever. I'm not sure the Angel's advice is helpful in deciphering its meaning (To þi saule it is gret damage.)

Interestingly (again) is swage:

"to shape or bend by use of a tool"

but that was later than your poem.

By the time of Milton's writing, swage did mean assuage.

Solution 3:

Google's definition includes:

• continue with great force or intensity.
  "the argument raged for days"
  synonyms: be violent, be at its height, be turbulent, be tempestuous, be uncontrollable, thunder, rampage "a tropical storm was raging"
• (of an illness or fire) spread very rapidly or uncontrollably.
  "the great cholera epidemic which raged across Europe in 1831"
• (of an emotion) have or reach a high degree of intensity.
  "she couldn't hide the fear that raged within her"

I think it means, like, "be intense" or "burn intensely like a fire".

It may also implies some uncontrollable insanity (from the Latin word for "rabies").

Solution 4:

It appears that the words play and rage were often paired in Middle English, the one word complementing the other.

Middle English Dictionary By Hans Kurath
_{^{CT abbreviation for Canterbury Tales}}

pleien (V)
2. (a) to play amorously; make love, engage in sexual intercourse

(al393) Gower CA 1.1764:
Thei were wedded in the nyht.. And sche began to plei and rage.

c1250 Body & S.(4) 29:
Bodi, þu ne mait nout lepen to plaien [vr. leiken] ne to rage.

5. (a) to make light or frivolous talk, jest, joke; ~with wordes, boast; in pleiinge wise, jestingly: (b) to make sport, tease: ~of, make fun of (sth.); ~upon, ridicule (sb.).

(c1390) Chaucer CT.Rv.A.3958:
Was noon..That with hire orste rage or ones pleye.

A New English Dictionary On Historical Principles, volume VIII, page 107

rage NOUN

6. A violent feeling, passion, or appetite. Also, violence, severity, height (of a feeling, etc.).
[…] b. Violent desire; sexual passion; heat.

?a 1366 Chaucer Rom. Rose 1657
When I was with this rage hent That caught hath many a man and shent.
1390 Gower Conf. 111.271
That ilke fyri rage in which that thei the lawe [of marriage] excede.
1500-20 Dunbar Poems 1xxxiv.8
Quhone the biche is jolie and on rage.

rage VERB (emphasis mine)

†3. To behave wantonly or riotously; to take one's pleasure, to play. Const with (a person).

• a 1300 Body & Soul in Map's poems 347

Body, miht thou nought lepen to playen ant rage.

• 1303 R.Brunne Handl. Synne 7896

To pley wyþ wommen and to rage.

• 1390 Gower Conf. I. 101

Sehe began to plei and to rage.

Solution 5:

Is it not me lyste (that is, my lust) that both play and rage. With sense of rage as in a fire burning. An adolescent response to the sight of the attractive woman that the angel is urging to be controlled.